diff --git a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
index 01b2eaf19d2..57a5a1f8ccd 100644
--- a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
+++ b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/diagnostics/coneDiagnosticToFirDiagnostic.kt
@@ -125,6 +125,7 @@ private fun ConeDiagnostic.toKtDiagnostic(
     is ConeDestructuringDeclarationsOnTopLevel -> null // TODO Currently a parsing error. Would be better to report here instead KT-58563
     is ConeCannotInferTypeParameterType -> FirErrors.CANNOT_INFER_PARAMETER_TYPE.createOn(source)
     is ConeCannotInferValueParameterType -> FirErrors.CANNOT_INFER_PARAMETER_TYPE.createOn(source)
+    is ConeCannotInferReceiverParameterType -> FirErrors.CANNOT_INFER_PARAMETER_TYPE.createOn(source)
     is ConeTypeVariableTypeIsNotInferred -> FirErrors.INFERENCE_ERROR.createOn(callOrAssignmentSource ?: source)
     is ConeInstanceAccessBeforeSuperCall -> FirErrors.INSTANCE_ACCESS_BEFORE_SUPER_CALL.createOn(source, this.target)
     is ConeStubDiagnostic -> null
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/FirCallCompleter.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/FirCallCompleter.kt
index 33d2e85e208..1d5f82e5653 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/FirCallCompleter.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/FirCallCompleter.kt
@@ -15,6 +15,8 @@ import org.jetbrains.kotlin.fir.declarations.FirFunction
 import org.jetbrains.kotlin.fir.declarations.FirResolvePhase
 import org.jetbrains.kotlin.fir.declarations.builder.buildContextReceiver
 import org.jetbrains.kotlin.fir.declarations.builder.buildValueParameter
+import org.jetbrains.kotlin.fir.diagnostics.ConeCannotInferReceiverParameterType
+import org.jetbrains.kotlin.fir.diagnostics.ConeCannotInferValueParameterType
 import org.jetbrains.kotlin.fir.expressions.*
 import org.jetbrains.kotlin.fir.resolve.ResolutionMode
 import org.jetbrains.kotlin.fir.resolve.calls.*
@@ -263,9 +265,9 @@ class FirCallCompleter(
                         containingFunctionSymbol = lambdaArgument.symbol
                         moduleData = session.moduleData
                         origin = FirDeclarationOrigin.Source
-                        returnTypeRef = itType.approximateLambdaInputType().toFirResolvedTypeRef()
                         this.name = name
                         symbol = FirValueParameterSymbol(name)
+                        returnTypeRef = itType.approximateLambdaInputType(symbol).toFirResolvedTypeRef()
                         defaultValue = null
                         isCrossinline = false
                         isNoinline = false
@@ -281,7 +283,7 @@ class FirCallCompleter(
                 receiverType == null -> lambdaArgument.replaceReceiverParameter(null)
                 !lambdaAtom.coerceFirstParameterToExtensionReceiver -> {
                     lambdaArgument.receiverParameter?.apply {
-                        val type = receiverType.approximateLambdaInputType()
+                        val type = receiverType.approximateLambdaInputType(valueParameter = null)
                         val source = source?.fakeElement(KtFakeSourceElementKind.ImplicitTypeRef)
                         replaceTypeRef(typeRef.resolvedTypeFromPrototype(type, source))
                     }
@@ -311,7 +313,7 @@ class FirCallCompleter(
                 else -> parameters
             }
             lambdaArgument.valueParameters.forEachIndexed { index, parameter ->
-                val newReturnType = theParameters[index].approximateLambdaInputType()
+                val newReturnType = theParameters[index].approximateLambdaInputType(parameter.symbol)
                 val newReturnTypeRef = if (parameter.returnTypeRef is FirImplicitTypeRef) {
                     newReturnType.toFirResolvedTypeRef(parameter.source?.fakeElement(KtFakeSourceElementKind.ImplicitReturnTypeOfLambdaValueParameter))
                 } else parameter.returnTypeRef.resolvedTypeFromPrototype(newReturnType)
@@ -352,10 +354,19 @@ class FirCallCompleter(
         }
     }
 
-    private fun ConeKotlinType.approximateLambdaInputType(): ConeKotlinType =
-        session.typeApproximator.approximateToSuperType(
+    private fun ConeKotlinType.approximateLambdaInputType(valueParameter: FirValueParameterSymbol?): ConeKotlinType {
+        // We only run lambda completion from ConstraintSystemCompletionContext.analyzeRemainingNotAnalyzedPostponedArgument when they are
+        // left uninferred.
+        // Currently, we use stub types for builder inference, so CANNOT_INFER_PARAMETER_TYPE is the only possible result here.
+        if (this is ConeTypeVariableType) {
+            val diagnostic = valueParameter?.let(::ConeCannotInferValueParameterType) ?: ConeCannotInferReceiverParameterType()
+            return ConeErrorType(diagnostic)
+        }
+
+        return session.typeApproximator.approximateToSuperType(
             this, TypeApproximatorConfiguration.FinalApproximationAfterResolutionAndInference
         ) ?: this
+    }
 }
 
 private fun Candidate.isFunctionForExpectTypeFromCastFeature(): Boolean {
diff --git a/compiler/fir/tree/src/org/jetbrains/kotlin/fir/diagnostics/ConeSimpleDiagnostic.kt b/compiler/fir/tree/src/org/jetbrains/kotlin/fir/diagnostics/ConeSimpleDiagnostic.kt
index 0414fd44404..77b22cf9e87 100644
--- a/compiler/fir/tree/src/org/jetbrains/kotlin/fir/diagnostics/ConeSimpleDiagnostic.kt
+++ b/compiler/fir/tree/src/org/jetbrains/kotlin/fir/diagnostics/ConeSimpleDiagnostic.kt
@@ -37,6 +37,10 @@ class ConeCannotInferValueParameterType(
     override val reason: String = "Cannot infer type for parameter ${valueParameter.name}"
 ) : ConeDiagnostic
 
+class ConeCannotInferReceiverParameterType(
+    override val reason: String = "Cannot infer type for receiver parameter"
+) : ConeDiagnostic
+
 class ConeTypeVariableTypeIsNotInferred(
     val typeVariableType: ConeTypeVariableType,
     override val reason: String = "Type for ${typeVariableType.lookupTag.debugName} is not inferred"
diff --git a/compiler/testData/diagnostics/tests/functionLiterals/kt47493.fir.kt b/compiler/testData/diagnostics/tests/functionLiterals/kt47493.fir.kt
deleted file mode 100644
index 9e4a8bb82c8..00000000000
--- a/compiler/testData/diagnostics/tests/functionLiterals/kt47493.fir.kt
+++ /dev/null
@@ -1,24 +0,0 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
-fun test1() {
-    try {
-        { toDouble ->
-        }
-    } catch (e: Exception) {
-
-    }
-}
-
-fun test2() {
-    try {
-
-    } catch (e: Exception) {
-        { toDouble ->
-        }
-    }
-}
-
-fun box(): String {
-    test1()
-    test2()
-    return "OK"
-}
diff --git a/compiler/testData/diagnostics/tests/functionLiterals/kt47493.kt b/compiler/testData/diagnostics/tests/functionLiterals/kt47493.kt
index c771ffa3583..cfc87118e04 100644
--- a/compiler/testData/diagnostics/tests/functionLiterals/kt47493.kt
+++ b/compiler/testData/diagnostics/tests/functionLiterals/kt47493.kt
@@ -1,4 +1,4 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
+// FIR_IDENTICAL
 fun test1() {
     try {
         { <!CANNOT_INFER_PARAMETER_TYPE!>toDouble<!> ->
diff --git a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
index 8531e9b4cdb..ec8755eebde 100644
--- a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !DIAGNOSTICS: -UNUSED_ANONYMOUS_PARAMETER -UNUSED_VARIABLE
 
 fun <T> select(vararg x: <!CANNOT_INFER_PARAMETER_TYPE, CANNOT_INFER_PARAMETER_TYPE!>T<!>) = x[0]
@@ -6,12 +5,12 @@ fun <K> id(x: K) = x
 
 fun main() {
     val x1 = select<Any?>(id { x, y -> }, { x: Int, y -> })
-    val x2 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(id { x, y -> }, { x: Int, y -> })
+    val x2 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(id { x, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> }, { x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> })
 
-    val x3 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(id(fun (x, y) {}), fun (x: Int, y) {})
+    val x3 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(id(fun (x, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}), fun (x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {})
 
     val x4 = select<Any?>((fun (x, y) {}), fun (x: Int, y) {})
-    val x5 = select<Any?>(id(fun (x, y) {}), fun (x: Int, y) {})
+    val x5 = select<Any?>(id(fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}), fun (x: Int, y) {})
     val x6 = id<Any?>(fun (x) {})
 
     select<Any?>(fun (x) {}, fun (x) {})
diff --git a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.kt b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.kt
index b525c0a82c2..0ba974cd9af 100644
--- a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.kt
+++ b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !DIAGNOSTICS: -UNUSED_ANONYMOUS_PARAMETER -UNUSED_VARIABLE
 
 fun <T> select(vararg x: T) = x[0]
diff --git a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
index 09f86b373c6..4a0a1e59823 100644
--- a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !DIAGNOSTICS: -UNUSED_PARAMETER
 
 fun callAny(arg: Any?) {}
@@ -20,14 +19,14 @@ fun testAnyCall() {
 }
 
 fun testParam() {
-    <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>callParam<!> {
-        param -> param
+    callParam {
+        <!CANNOT_INFER_PARAMETER_TYPE!>param<!> -> param
     }
 }
 
 fun testParamCall() {
     callParam {
-        param -> <!UNRESOLVED_REFERENCE!>param<!>()
+        <!CANNOT_INFER_PARAMETER_TYPE!>param<!> -> <!UNRESOLVED_REFERENCE!>param<!>()
     }
 }
 
diff --git a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.kt b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.kt
index 10869fe484f..630d0a7a116 100644
--- a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.kt
+++ b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !DIAGNOSTICS: -UNUSED_PARAMETER
 
 fun callAny(arg: Any?) {}
diff --git a/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.fir.kt b/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.fir.kt
index 4bd1452346e..1552b559c59 100644
--- a/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.fir.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !LANGUAGE: +PartiallySpecifiedTypeArguments
 // !DIAGNOSTICS: -UNCHECKED_CAST
 // WITH_STDLIB
diff --git a/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.kt b/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.kt
index 153eb3d4b21..a70dcfef95c 100644
--- a/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.kt
+++ b/compiler/testData/diagnostics/tests/inference/underscoredTypeInForbiddenPositions.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // !LANGUAGE: +PartiallySpecifiedTypeArguments
 // !DIAGNOSTICS: -UNCHECKED_CAST
 // WITH_STDLIB
diff --git a/compiler/testData/diagnostics/tests/kt49438.fir.kt b/compiler/testData/diagnostics/tests/kt49438.fir.kt
index e2cd65b37f7..113c45a9f6b 100644
--- a/compiler/testData/diagnostics/tests/kt49438.fir.kt
+++ b/compiler/testData/diagnostics/tests/kt49438.fir.kt
@@ -1,3 +1,7 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 fun <K> foo(x: K) {}
-val x = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { it.<!UNRESOLVED_REFERENCE!>toFloat<!>() }
+val x1 = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { it.<!UNRESOLVED_REFERENCE!>toFloat<!>() }
+val x2 = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> it.<!UNRESOLVED_REFERENCE!>toFloat<!>() }
+val x3 = foo<<!UNRESOLVED_REFERENCE!>unresolved<!>.() -> Float> { this.<!UNRESOLVED_REFERENCE!>toFloat<!>() }
+val x4 = foo<(Array<<!UNRESOLVED_REFERENCE!>unresolved<!>>) -> Int> { it.size }
+
+fun <T> bar() = foo<(T) -> String> { it.toString() }
diff --git a/compiler/testData/diagnostics/tests/kt49438.kt b/compiler/testData/diagnostics/tests/kt49438.kt
index 6b0c6468dde..2af24cd1cb7 100644
--- a/compiler/testData/diagnostics/tests/kt49438.kt
+++ b/compiler/testData/diagnostics/tests/kt49438.kt
@@ -1,3 +1,7 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 fun <K> foo(x: K) {}
-val x = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>it<!>.<!DEBUG_INFO_MISSING_UNRESOLVED!>toFloat<!>() }
+val x1 = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>it<!>.<!DEBUG_INFO_MISSING_UNRESOLVED!>toFloat<!>() }
+val x2 = foo<(<!UNRESOLVED_REFERENCE!>unresolved<!>) -> Float> { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>it<!>.<!DEBUG_INFO_MISSING_UNRESOLVED!>toFloat<!>() }
+val x3 = foo<<!UNRESOLVED_REFERENCE!>unresolved<!>.() -> Float> { this.<!DEBUG_INFO_MISSING_UNRESOLVED!>toFloat<!>() }
+val x4 = foo<(Array<<!UNRESOLVED_REFERENCE!>unresolved<!>>) -> Int> { <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>it<!>.size }
+
+fun <T> bar() = foo<(T) -> String> { it.toString() }
diff --git a/compiler/testData/diagnostics/tests/kt49438.txt b/compiler/testData/diagnostics/tests/kt49438.txt
index 6b52f887c58..423cc8dac6e 100644
--- a/compiler/testData/diagnostics/tests/kt49438.txt
+++ b/compiler/testData/diagnostics/tests/kt49438.txt
@@ -1,4 +1,8 @@
 package
 
-public val x: kotlin.Unit
+public val x1: kotlin.Unit
+public val x2: kotlin.Unit
+public val x3: kotlin.Unit
+public val x4: kotlin.Unit
+public fun </*0*/ T> bar(): kotlin.Unit
 public fun </*0*/ K> foo(/*0*/ x: K): kotlin.Unit
diff --git a/compiler/testData/diagnostics/tests/regressions/kt10843.fir.kt b/compiler/testData/diagnostics/tests/regressions/kt10843.fir.kt
index 0452510818f..1c12ce604e4 100644
--- a/compiler/testData/diagnostics/tests/regressions/kt10843.fir.kt
+++ b/compiler/testData/diagnostics/tests/regressions/kt10843.fir.kt
@@ -1,8 +1,7 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // NI_EXPECTED_FILE
 // See EA-76890 / KT-10843: NPE during analysis
 fun lambda(x : Int?) = x?.<!FUNCTION_CALL_EXPECTED!>let<!> <!UNRESOLVED_REFERENCE!>l<!> {
-    y ->
+    <!CANNOT_INFER_PARAMETER_TYPE!>y<!> ->
     if (y <!UNRESOLVED_REFERENCE!>><!> 0) return@l x
     y
 }<!NOT_NULL_ASSERTION_ON_LAMBDA_EXPRESSION!>!!<!>
diff --git a/compiler/testData/diagnostics/tests/regressions/kt10843.kt b/compiler/testData/diagnostics/tests/regressions/kt10843.kt
index 50718c08ebb..50a313b667b 100644
--- a/compiler/testData/diagnostics/tests/regressions/kt10843.kt
+++ b/compiler/testData/diagnostics/tests/regressions/kt10843.kt
@@ -1,4 +1,3 @@
-// IGNORE_LEAKED_INTERNAL_TYPES: KT-54568
 // NI_EXPECTED_FILE
 // See EA-76890 / KT-10843: NPE during analysis
 fun lambda(x : Int?) = x?.<!FUNCTION_CALL_EXPECTED, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NO_VALUE_FOR_PARAMETER!>let<!> <!DEBUG_INFO_MISSING_UNRESOLVED!>l<!> {