diff --git a/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.kt b/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.kt
new file mode 100644
index 00000000000..71a3c91a16e
--- /dev/null
+++ b/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.kt
@@ -0,0 +1,40 @@
+// !CHECK_TYPE
+// ISSUE: KT-37070
+
+class KotlinClass(private val name: String) : Comparable<KotlinClass> {
+    override operator fun compareTo(that: KotlinClass): Int {
+        return name.compareTo(that.name)
+    }
+}
+
+
+// TESTCASE NUMBER: 1
+fun case1(kotlinClass: KotlinClass?) {
+
+    val value = kotlinClass?.let {
+        it
+    }
+
+    value.checkType { _<KotlinClass?>() }
+
+    val lambda = kotlinClass?.let {
+        {<!UNRESOLVED_REFERENCE!>it<!>}
+    }
+
+    lambda.checkType { <!INAPPLICABLE_CANDIDATE!>_<!><Function1<Unit, KotlinClass?>>() }
+}
+// TESTCASE NUMBER: 2
+fun case2(kotlinClass: KotlinClass) {
+
+    val value = kotlinClass.let {
+        it
+    }
+
+    value.checkType { _<KotlinClass>() }
+
+    val lambda = kotlinClass.let {
+        {<!UNRESOLVED_REFERENCE!>it<!>}
+    }
+
+    lambda.checkType { <!INAPPLICABLE_CANDIDATE!>_<!><Function1<Unit, KotlinClass?>>() }
+}
\ No newline at end of file
diff --git a/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.txt b/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.txt
new file mode 100644
index 00000000000..d3ccf247c59
--- /dev/null
+++ b/compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.txt
@@ -0,0 +1,70 @@
+FILE: lambdaArgInScopeFunction.kt
+    public final class KotlinClass : R|kotlin/Comparable<KotlinClass>| {
+        public constructor(name: R|kotlin/String|): R|KotlinClass| {
+            super<R|kotlin/Any|>()
+        }
+
+        private final val name: R|kotlin/String| = R|<local>/name|
+            private get(): R|kotlin/String|
+
+        public final override operator fun compareTo(that: R|KotlinClass|): R|kotlin/Int| {
+            ^compareTo this@R|/KotlinClass|.R|/KotlinClass.name|.R|kotlin/String.compareTo|(R|<local>/that|.R|/KotlinClass.name|)
+        }
+
+    }
+    public final fun case1(kotlinClass: R|KotlinClass?|): R|kotlin/Unit| {
+        lval value: R|KotlinClass?| = R|<local>/kotlinClass|?.R|kotlin/let|<R|KotlinClass|, R|KotlinClass|>(<L> = let@fun <anonymous>(it: R|KotlinClass|): R|KotlinClass| <kind=EXACTLY_ONCE>  {
+            ^ R|<local>/it|
+        }
+        )
+        R|<local>/value|.R|tests/_checkType/checkType|<R|KotlinClass?|>(<L> = checkType@fun R|tests/_checkType/Inv<KotlinClass?>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|KotlinClass?|>()
+        }
+        )
+        lval lambda: R|kotlin/Nothing?| = R|<local>/kotlinClass|?.R|kotlin/let|<R|KotlinClass|, R|kotlin/Nothing|>(<L> = let@fun <anonymous>(it: R|KotlinClass|): R|kotlin/Nothing| <kind=EXACTLY_ONCE>  {
+            ^ let@fun <anonymous>(): <ERROR TYPE REF: Unresolved name: it> {
+                ^ <Unresolved name: it>#
+            }
+
+        }
+        )
+        R|<local>/lambda|.R|tests/_checkType/checkType|<R|kotlin/Nothing?|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Nothing?>|.<anonymous>(): R|kotlin/Unit| {
+            ^ <Inapplicable(WRONG_RECEIVER): [tests/_checkType/_]>#<R|(kotlin/Unit) -> KotlinClass?|>()
+        }
+        )
+    }
+    public final fun case2(kotlinClass: R|KotlinClass|): R|kotlin/Unit| {
+        lval value: R|KotlinClass| = R|<local>/kotlinClass|.R|kotlin/let|<R|KotlinClass|, R|KotlinClass|>(<L> = let@fun <anonymous>(it: R|KotlinClass|): R|KotlinClass| <kind=EXACTLY_ONCE>  {
+            ^ R|<local>/it|
+        }
+        )
+        R|<local>/value|.R|tests/_checkType/checkType|<R|KotlinClass|>(<L> = checkType@fun R|tests/_checkType/Inv<KotlinClass>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|KotlinClass|>()
+        }
+        )
+        lval lambda: R|kotlin/Nothing| = R|<local>/kotlinClass|.R|kotlin/let|<R|KotlinClass|, R|kotlin/Nothing|>(<L> = let@fun <anonymous>(it: R|KotlinClass|): R|kotlin/Nothing| <kind=EXACTLY_ONCE>  {
+            ^ let@fun <anonymous>(): <ERROR TYPE REF: Unresolved name: it> {
+                ^ <Unresolved name: it>#
+            }
+
+        }
+        )
+        R|<local>/lambda|.R|tests/_checkType/checkType|<R|kotlin/Nothing|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Nothing>|.<anonymous>(): R|kotlin/Unit| {
+            ^ <Inapplicable(WRONG_RECEIVER): [tests/_checkType/_]>#<R|(kotlin/Unit) -> KotlinClass?|>()
+        }
+        )
+    }
+FILE: CHECK_TYPE.kt
+    public final fun <T> checkSubtype(t: R|T|): R|T| {
+        ^checkSubtype R|<local>/t|
+    }
+    public final class Inv<T> : R|kotlin/Any| {
+        public constructor<T>(): R|tests/_checkType/Inv<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public final fun <E> R|tests/_checkType/Inv<E>|._(): R|kotlin/Unit| {
+    }
+    public final infix fun <T> R|T|.checkType(f: R|tests/_checkType/Inv<T>.() -> kotlin/Unit|): R|kotlin/Unit| {
+    }
diff --git a/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.kt b/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.kt
new file mode 100644
index 00000000000..77d58e48972
--- /dev/null
+++ b/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.kt
@@ -0,0 +1,71 @@
+// !CHECK_TYPE
+// UNEXPECTED BEHAVIOUR
+// ISSUES: KT-37066
+
+// TESTCASE NUMBER: 1
+// FILE: JavaClass.java
+public final class JavaClass implements Comparable<JavaClass> {
+    private final String name;
+
+    public JavaClass (String name) {
+        this.name = name;
+    }
+
+    @Override
+    public int compareTo(JavaClass that) {
+        return this.name.compareTo(that.name);
+    }
+}
+
+
+// FILE: KotlinClass.kt
+fun case1(javaClass: JavaClass?) {
+    val validType: (JavaClass) -> Boolean = if (javaClass != null) { it -> it == javaClass } else BooCase1.FILTER
+
+    val invalidType = if (javaClass != null) { it -> it == javaClass } else BooCase1.FILTER
+
+    validType.checkType { _<Function1<JavaClass, Boolean>>() } //ok
+
+    invalidType.checkType { _<Function1<Nothing, Boolean>>() } //(!!!)
+
+    Case1(javaClass).x.checkType { _<Function1<Nothing, Boolean>>() } //(!!!)
+}
+
+class Case1(val javaClass: JavaClass?) {
+    val x = if (javaClass != null) { it -> it == javaClass } else BooCase2.FILTER
+}
+
+class BooCase1() {
+    companion object {
+        val FILTER: (JavaClass) -> Boolean = { true }
+    }
+}
+
+// TESTCASE NUMBER: 2
+
+class KotlinClass(private val name: String) : Comparable<KotlinClass> {
+    override operator fun compareTo(that: KotlinClass): Int {
+        return name.compareTo(that.name)
+    }
+}
+
+fun case2(kotlinClass: KotlinClass?) {
+    val validType: (KotlinClass) -> Boolean = if (kotlinClass != null) { it -> it == kotlinClass } else BooCase2.FILTER
+    val invalidType = if (kotlinClass != null) { it -> it == kotlinClass } else BooCase2.FILTER
+
+    validType.checkType { _<Function1<KotlinClass, Boolean>>() } //ok
+
+    invalidType.checkType { _<Function1<Nothing, Boolean>>() }  //(!!!)
+
+    Case2(kotlinClass).x.checkType { _<Function1<Nothing, Boolean>>() } //(!!!)
+}
+
+class Case2(val kotlinClass: KotlinClass?) {
+    val x = if (kotlinClass != null) { it -> it == kotlinClass } else BooCase2.FILTER
+}
+
+class BooCase2() {
+    companion object {
+        val FILTER: (KotlinClass) -> Boolean = { true }
+    }
+}
diff --git a/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.txt b/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.txt
new file mode 100644
index 00000000000..528aa86de97
--- /dev/null
+++ b/compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.txt
@@ -0,0 +1,188 @@
+FILE: KotlinClass.kt
+    public final fun case1(javaClass: R|JavaClass?|): R|kotlin/Unit| {
+        lval validType: R|(JavaClass) -> kotlin/Boolean| = when () {
+            !=(R|<local>/javaClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/javaClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase1|.R|/BooCase1.Companion.FILTER|
+            }
+        }
+
+        lval invalidType: R|(kotlin/Nothing) -> kotlin/Boolean| = when () {
+            !=(R|<local>/javaClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/javaClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase1|.R|/BooCase1.Companion.FILTER|
+            }
+        }
+
+        R|<local>/validType|.R|tests/_checkType/checkType|<R|(JavaClass) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<JavaClass, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(JavaClass) -> kotlin/Boolean|>()
+        }
+        )
+        R|<local>/invalidType|.R|tests/_checkType/checkType|<R|(kotlin/Nothing) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<kotlin/Nothing, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(kotlin/Nothing) -> kotlin/Boolean|>()
+        }
+        )
+        R|/Case1.Case1|(R|<local>/javaClass|).R|/Case1.x|.R|tests/_checkType/checkType|<R|(kotlin/Nothing) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<kotlin/Nothing, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(kotlin/Nothing) -> kotlin/Boolean|>()
+        }
+        )
+    }
+    public final class Case1 : R|kotlin/Any| {
+        public constructor(javaClass: R|JavaClass?|): R|Case1| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final val javaClass: R|JavaClass?| = R|<local>/javaClass|
+            public get(): R|JavaClass?|
+
+        public final val x: R|(kotlin/Nothing) -> kotlin/Boolean| = when () {
+            !=(R|<local>/javaClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/javaClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase2|.R|/BooCase2.Companion.FILTER|
+            }
+        }
+
+            public get(): R|(kotlin/Nothing) -> kotlin/Boolean|
+
+    }
+    public final class BooCase1 : R|kotlin/Any| {
+        public constructor(): R|BooCase1| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final companion object Companion : R|kotlin/Any| {
+            private constructor(): R|BooCase1.Companion| {
+                super<R|kotlin/Any|>()
+            }
+
+            public final val FILTER: R|(JavaClass) -> kotlin/Boolean| = fun <anonymous>(it: R|JavaClass|): R|kotlin/Boolean| {
+                ^ Boolean(true)
+            }
+
+                public get(): R|(JavaClass) -> kotlin/Boolean|
+
+        }
+
+    }
+    public final class KotlinClass : R|kotlin/Comparable<KotlinClass>| {
+        public constructor(name: R|kotlin/String|): R|KotlinClass| {
+            super<R|kotlin/Any|>()
+        }
+
+        private final val name: R|kotlin/String| = R|<local>/name|
+            private get(): R|kotlin/String|
+
+        public final override operator fun compareTo(that: R|KotlinClass|): R|kotlin/Int| {
+            ^compareTo this@R|/KotlinClass|.R|/KotlinClass.name|.R|kotlin/String.compareTo|(R|<local>/that|.R|/KotlinClass.name|)
+        }
+
+    }
+    public final fun case2(kotlinClass: R|KotlinClass?|): R|kotlin/Unit| {
+        lval validType: R|(KotlinClass) -> kotlin/Boolean| = when () {
+            !=(R|<local>/kotlinClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/kotlinClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase2|.R|/BooCase2.Companion.FILTER|
+            }
+        }
+
+        lval invalidType: R|(kotlin/Nothing) -> kotlin/Boolean| = when () {
+            !=(R|<local>/kotlinClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/kotlinClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase2|.R|/BooCase2.Companion.FILTER|
+            }
+        }
+
+        R|<local>/validType|.R|tests/_checkType/checkType|<R|(KotlinClass) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<KotlinClass, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(KotlinClass) -> kotlin/Boolean|>()
+        }
+        )
+        R|<local>/invalidType|.R|tests/_checkType/checkType|<R|(kotlin/Nothing) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<kotlin/Nothing, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(kotlin/Nothing) -> kotlin/Boolean|>()
+        }
+        )
+        R|/Case2.Case2|(R|<local>/kotlinClass|).R|/Case2.x|.R|tests/_checkType/checkType|<R|(kotlin/Nothing) -> kotlin/Boolean|>(<L> = checkType@fun R|tests/_checkType/Inv<kotlin/Function1<kotlin/Nothing, kotlin/Boolean>>|.<anonymous>(): R|kotlin/Unit| {
+            this@R|special/anonymous|.R|tests/_checkType/_|<R|(kotlin/Nothing) -> kotlin/Boolean|>()
+        }
+        )
+    }
+    public final class Case2 : R|kotlin/Any| {
+        public constructor(kotlinClass: R|KotlinClass?|): R|Case2| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final val kotlinClass: R|KotlinClass?| = R|<local>/kotlinClass|
+            public get(): R|KotlinClass?|
+
+        public final val x: R|(kotlin/Nothing) -> kotlin/Boolean| = when () {
+            !=(R|<local>/kotlinClass|, Null(null)) ->  {
+                fun <anonymous>(it: R|kotlin/Nothing|): R|kotlin/Boolean| {
+                    ^ ==(R|<local>/it|, R|<local>/kotlinClass|)
+                }
+
+            }
+            else ->  {
+                Q|BooCase2|.R|/BooCase2.Companion.FILTER|
+            }
+        }
+
+            public get(): R|(kotlin/Nothing) -> kotlin/Boolean|
+
+    }
+    public final class BooCase2 : R|kotlin/Any| {
+        public constructor(): R|BooCase2| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final companion object Companion : R|kotlin/Any| {
+            private constructor(): R|BooCase2.Companion| {
+                super<R|kotlin/Any|>()
+            }
+
+            public final val FILTER: R|(KotlinClass) -> kotlin/Boolean| = fun <anonymous>(it: R|KotlinClass|): R|kotlin/Boolean| {
+                ^ Boolean(true)
+            }
+
+                public get(): R|(KotlinClass) -> kotlin/Boolean|
+
+        }
+
+    }
+FILE: CHECK_TYPE.kt
+    public final fun <T> checkSubtype(t: R|T|): R|T| {
+        ^checkSubtype R|<local>/t|
+    }
+    public final class Inv<T> : R|kotlin/Any| {
+        public constructor<T>(): R|tests/_checkType/Inv<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public final fun <E> R|tests/_checkType/Inv<E>|._(): R|kotlin/Unit| {
+    }
+    public final infix fun <T> R|T|.checkType(f: R|tests/_checkType/Inv<T>.() -> kotlin/Unit|): R|kotlin/Unit| {
+    }
diff --git a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
index 520c073e471..29e1d2359bf 100644
--- a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
+++ b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsTestGenerated.java
@@ -218,6 +218,16 @@ public class FirDiagnosticsTestGenerated extends AbstractFirDiagnosticsTest {
         runTest("compiler/fir/resolve/testData/resolve/javaStaticScopeInheritance.kt");
     }
 
+    @TestMetadata("lambdaArgInScopeFunction.kt")
+    public void testLambdaArgInScopeFunction() throws Exception {
+        runTest("compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.kt");
+    }
+
+    @TestMetadata("lambdaPropertyTypeInference.kt")
+    public void testLambdaPropertyTypeInference() throws Exception {
+        runTest("compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.kt");
+    }
+
     @TestMetadata("localFunctionsHiding.kt")
     public void testLocalFunctionsHiding() throws Exception {
         runTest("compiler/fir/resolve/testData/resolve/localFunctionsHiding.kt");
diff --git a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
index 6bb37555d5d..2f073cf5dc7 100644
--- a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
+++ b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsWithLightTreeTestGenerated.java
@@ -218,6 +218,16 @@ public class FirDiagnosticsWithLightTreeTestGenerated extends AbstractFirDiagnos
         runTest("compiler/fir/resolve/testData/resolve/javaStaticScopeInheritance.kt");
     }
 
+    @TestMetadata("lambdaArgInScopeFunction.kt")
+    public void testLambdaArgInScopeFunction() throws Exception {
+        runTest("compiler/fir/resolve/testData/resolve/lambdaArgInScopeFunction.kt");
+    }
+
+    @TestMetadata("lambdaPropertyTypeInference.kt")
+    public void testLambdaPropertyTypeInference() throws Exception {
+        runTest("compiler/fir/resolve/testData/resolve/lambdaPropertyTypeInference.kt");
+    }
+
     @TestMetadata("localFunctionsHiding.kt")
     public void testLocalFunctionsHiding() throws Exception {
         runTest("compiler/fir/resolve/testData/resolve/localFunctionsHiding.kt");