diff --git a/org.eclipse.jdt.core.manipulation/core extension/org/eclipse/jdt/internal/corext/fix/LambdaExpressionsFixCore.java b/org.eclipse.jdt.core.manipulation/core extension/org/eclipse/jdt/internal/corext/fix/LambdaExpressionsFixCore.java
index 844c6ce9b1d..29d5a5c3f15 100644
--- a/org.eclipse.jdt.core.manipulation/core extension/org/eclipse/jdt/internal/corext/fix/LambdaExpressionsFixCore.java	
+++ b/org.eclipse.jdt.core.manipulation/core extension/org/eclipse/jdt/internal/corext/fix/LambdaExpressionsFixCore.java	
@@ -945,7 +945,7 @@ public boolean visit(final ThisExpression node) {
 				}
 
 				ITypeBinding targetTypeBinding= ASTNodes.getTargetType(classInstanceCreation);
-				if (ASTNodes.isTargetAmbiguous(classInstanceCreation, ASTNodes.isExplicitlyTypedLambda(cicReplacement)) || targetTypeBinding.getFunctionalInterfaceMethod() == null) {
+				if (needCastForWildcardArgument(classInstanceCreation) || ASTNodes.isTargetAmbiguous(classInstanceCreation, ASTNodes.isExplicitlyTypedLambda(cicReplacement)) || targetTypeBinding.getFunctionalInterfaceMethod() == null) {
 					CastExpression cast= ast.newCastExpression();
 					cast.setExpression(cicReplacement);
 					ImportRewrite importRewrite= cuRewrite.getImportRewrite();
@@ -962,6 +962,49 @@ public boolean visit(final ThisExpression node) {
 			}
 		}
 
+		private boolean needCastForWildcardArgument(ClassInstanceCreation classInstanceCreation) {
+			if (classInstanceCreation.getLocationInParent() == MethodInvocation.ARGUMENTS_PROPERTY) {
+				MethodInvocation parent= (MethodInvocation)classInstanceCreation.getParent();
+				List<Expression> arguments= parent.arguments();
+				IMethodBinding methodBinding= parent.resolveMethodBinding();
+				if (methodBinding != null) {
+					ITypeBinding[] parameterTypes= methodBinding.getParameterTypes();
+					int index= -1;
+					for (int i= 0; i < arguments.size(); ++i) {
+						if (arguments.get(i) == classInstanceCreation) {
+							index= i;
+							break;
+						}
+					}
+					if (index >= 0) {
+						ITypeBinding parameterTypeBinding= null;
+						if (index < parameterTypes.length) {
+							parameterTypeBinding= parameterTypes[index];
+						} else {
+							parameterTypeBinding= parameterTypes[parameterTypes.length - 1].getComponentType();
+						}
+						ITypeBinding classInstanceParameterizedType= classInstanceCreation.getType().resolveBinding();
+						ITypeBinding[] classInstanceTypeArguments= classInstanceParameterizedType.getTypeArguments();
+						ITypeBinding[] typeArguments= parameterTypeBinding.getTypeArguments();
+						for (int i= 0; i < typeArguments.length; ++i) {
+							ITypeBinding typeArgument= typeArguments[i];
+							if (typeArgument.isWildcardType()) {
+								ITypeBinding bound= typeArgument.getBound();
+								if (bound == null) {
+									bound= typeArgument.getErasure();
+								}
+								ITypeBinding classInstanceTypeArgument= classInstanceTypeArguments[i];
+								if (!bound.isSubTypeCompatible(classInstanceTypeArgument)) {
+									return true;
+								}
+							}
+						}
+					}
+				}
+			}
+			return false;
+		}
+
 		private Expression castMethodRefIfNeeded(final CompilationUnitRewrite cuRewrite, AST ast, Expression methodRef, Expression visited) {
 			boolean needCast= false;
 			Expression replacementNode= methodRef;
diff --git a/org.eclipse.jdt.ui.tests/ui/org/eclipse/jdt/ui/tests/quickfix/CleanUpTest1d8.java b/org.eclipse.jdt.ui.tests/ui/org/eclipse/jdt/ui/tests/quickfix/CleanUpTest1d8.java
index 62f2a0eaf1e..605b63d4a4e 100644
--- a/org.eclipse.jdt.ui.tests/ui/org/eclipse/jdt/ui/tests/quickfix/CleanUpTest1d8.java
+++ b/org.eclipse.jdt.ui.tests/ui/org/eclipse/jdt/ui/tests/quickfix/CleanUpTest1d8.java
@@ -6925,4 +6925,132 @@ public String get() {
 		assertRefactoringResultAsExpected(new ICompilationUnit[] { cu1 }, new String[] { expected1 }, null);
     }
 
+	@Test
+	public void testConvertToLambdaIssue1535_1() throws Exception {
+		IPackageFragment pack1= fSourceFolder.createPackageFragment("test1", false, null);
+		String original= """
+				package test1;
+
+				import java.util.Iterator;
+				import java.util.List;
+
+				public class E {
+					private void func(Iterable<?> a, Iterable<?> b) {}
+					private void assertIteratorProducesExpectedList(
+						List<String> expectedList,
+						Iterator<String> rankedListIterator) {
+						func(expectedList, new Iterable<String>() {
+							@Override
+							public Iterator<String> iterator() {
+                				return rankedListIterator;
+							}
+						});
+					}
+				}
+				""";
+		ICompilationUnit cu1= pack1.createCompilationUnit("E.java", original, false, null);
+
+		enable(CleanUpConstants.CONVERT_FUNCTIONAL_INTERFACES);
+		enable(CleanUpConstants.USE_LAMBDA);
+
+		String expected= """
+				package test1;
+
+				import java.util.Iterator;
+				import java.util.List;
+
+				public class E {
+					private void func(Iterable<?> a, Iterable<?> b) {}
+					private void assertIteratorProducesExpectedList(
+						List<String> expectedList,
+						Iterator<String> rankedListIterator) {
+						func(expectedList, (Iterable<String>) () -> rankedListIterator);
+					}
+				}
+				""";
+
+		assertRefactoringResultAsExpected(new ICompilationUnit[] { cu1 }, new String[] { expected }, null);
+
+	}
+
+	@Test
+	public void testConvertToLambdaIssue1535_2() throws Exception {
+		IPackageFragment pack1= fSourceFolder.createPackageFragment("test1", false, null);
+		String original= """
+				package test1;
+
+				import java.util.Iterator;
+				import java.util.List;
+
+				public class E {
+					private void func(Iterable<?> a, Iterable<?> b) {}
+
+					private Iterator<String> myfunc() {
+						class K implements Iterator<String> {
+							@Override
+							public boolean hasNext() {
+								return false;
+							}
+
+							@Override
+							public String next() {
+								return null;
+							}
+						}
+						return new K();
+					}
+
+					private void assertIteratorProducesExpectedList(
+						List<String> expectedList,
+						Iterator<String> rankedListIterator) {
+						func(expectedList, new Iterable<String>() {
+							@Override
+							public Iterator<String> iterator() {
+                				return myfunc();
+							}
+						});
+					}
+				}
+				""";
+		ICompilationUnit cu1= pack1.createCompilationUnit("E.java", original, false, null);
+
+		enable(CleanUpConstants.CONVERT_FUNCTIONAL_INTERFACES);
+		enable(CleanUpConstants.USE_LAMBDA);
+		enable(CleanUpConstants.ALSO_SIMPLIFY_LAMBDA);
+
+		String expected= """
+				package test1;
+
+				import java.util.Iterator;
+				import java.util.List;
+
+				public class E {
+					private void func(Iterable<?> a, Iterable<?> b) {}
+
+					private Iterator<String> myfunc() {
+						class K implements Iterator<String> {
+							@Override
+							public boolean hasNext() {
+								return false;
+							}
+
+							@Override
+							public String next() {
+								return null;
+							}
+						}
+						return new K();
+					}
+
+					private void assertIteratorProducesExpectedList(
+						List<String> expectedList,
+						Iterator<String> rankedListIterator) {
+						func(expectedList, (Iterable<String>) this::myfunc);
+					}
+				}
+				""";
+
+		assertRefactoringResultAsExpected(new ICompilationUnit[] { cu1 }, new String[] { expected }, null);
+
+	}
 }