diff --git a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/CFGBuilder.java b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/CFGBuilder.java
index 5ec94c79c200..bd27ca4d1c61 100644
--- a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/CFGBuilder.java
+++ b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/CFGBuilder.java
@@ -690,7 +690,10 @@ public class CFGBuilder {
     }
     // Unknown function
     flushFields();
-    PsiType returnType = LambdaUtil.getFunctionalInterfaceReturnType(functionalExpression.getType());
+    myAnalyzer.addConditionalRuntimeThrow();
+    PsiType functionalInterfaceType = functionalExpression.getType();
+    myAnalyzer.addMethodThrows(LambdaUtil.getFunctionalInterfaceMethod(functionalInterfaceType), null);
+    PsiType returnType = LambdaUtil.getFunctionalInterfaceReturnType(functionalInterfaceType);
     if (returnType != null) {
       push(getFactory().createTypeValue(returnType, DfaPsiUtil.getTypeNullability(returnType)));
     }
diff --git a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/ControlFlowAnalyzer.java b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/ControlFlowAnalyzer.java
index 3b5775eeb66f..24c65a6cb1a1 100644
--- a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/ControlFlowAnalyzer.java
+++ b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/ControlFlowAnalyzer.java
@@ -1041,7 +1041,7 @@ public class ControlFlowAnalyzer extends JavaElementVisitor {
     finishElement(statement);
   }
 
-  private void addConditionalRuntimeThrow() {
+  void addConditionalRuntimeThrow() {
     if (!shouldHandleException()) {
       return;
     }
@@ -1655,8 +1655,8 @@ public class ControlFlowAnalyzer extends JavaElementVisitor {
     finishElement(expression);
   }
 
-  private void addMethodThrows(PsiMethod method, @Nullable PsiElement explicitCall) {
-    if (method != null) {
+  void addMethodThrows(PsiMethod method, @Nullable PsiElement explicitCall) {
+    if (method != null && shouldHandleException()) {
       addThrows(explicitCall, method.getThrowsList().getReferencedTypes());
     }
   }
@@ -1774,9 +1774,7 @@ public class ControlFlowAnalyzer extends JavaElementVisitor {
       ifNotFail.setOffset(myCurrentFlow.getInstructionCount());
     }
 
-    if (shouldHandleException()) {
-      addMethodThrows(method, anchor);
-    }
+    addMethodThrows(method, anchor);
   }
 
   /**
@@ -1862,9 +1860,7 @@ public class ControlFlowAnalyzer extends JavaElementVisitor {
       List<? extends MethodContract> contracts = constructor == null ? Collections.emptyList() : JavaMethodContractUtil.getMethodContracts(constructor);
       addInstruction(new MethodCallInstruction(expression, precalculatedNewValue, contracts));
 
-      if (shouldHandleException()) {
-        addMethodThrows(constructor, expression);
-      }
+      addMethodThrows(constructor, expression);
     }
 
     finishElement(expression);
diff --git a/java/java-tests/testData/inspection/dataFlow/fixture/MapUpdateInlining.java b/java/java-tests/testData/inspection/dataFlow/fixture/MapUpdateInlining.java
index d1486277bb3e..66f062b18602 100644
--- a/java/java-tests/testData/inspection/dataFlow/fixture/MapUpdateInlining.java
+++ b/java/java-tests/testData/inspection/dataFlow/fixture/MapUpdateInlining.java
@@ -2,6 +2,7 @@ import foo.*;
 
 import java.util.Map;
 import java.util.HashMap;
+import java.util.function.Function;
 
 class MapUpdateInlining {
   void testKey(Map<String, String> map) {
@@ -82,4 +83,22 @@ class MapUpdateInlining {
   }
 
   native void doSmth();
+
+  // IDEA-204641
+  public static void testAnyLambda(@NotNull Function<String, String> lambda) {
+    Map<String, String> map = new HashMap<>();
+    Throwable thrown = null;
+    try {
+      map.computeIfAbsent("a", lambda);
+    }
+    catch (Throwable t) {
+      thrown = t;
+      throw t;
+    }
+    finally {
+      if (thrown != null) { // possible
+        int x = 0;
+      }
+    }
+  }
 }