diff --git a/js/src/frontend/BytecodeCompiler.cpp b/js/src/frontend/BytecodeCompiler.cpp
index 059408ba152..5d04b17b4e2 100644
--- a/js/src/frontend/BytecodeCompiler.cpp
+++ b/js/src/frontend/BytecodeCompiler.cpp
@@ -454,6 +454,8 @@ frontend::CompileLazyFunction(JSContext *cx, LazyScript *lazy, const jschar *cha
         script->directlyInsideEval = true;
     if (lazy->usesArgumentsAndApply())
         script->usesArgumentsAndApply = true;
+    if (lazy->hasBeenCloned())
+        script->hasBeenCloned = true;
 
     BytecodeEmitter bce(/* parent = */ nullptr, &parser, pn->pn_funbox, script, options.forEval,
                         /* evalCaller = */ NullPtr(), /* hasGlobalScope = */ true,
@@ -461,6 +463,9 @@ frontend::CompileLazyFunction(JSContext *cx, LazyScript *lazy, const jschar *cha
     if (!bce.init())
         return false;
 
+    if (lazy->treatAsRunOnce())
+        bce.lazyRunOnceLambda = true;
+
     return EmitFunctionScript(cx, &bce, pn->pn_body);
 }
 
diff --git a/js/src/frontend/BytecodeEmitter.cpp b/js/src/frontend/BytecodeEmitter.cpp
index 8af8e3fe31e..41321641b91 100644
--- a/js/src/frontend/BytecodeEmitter.cpp
+++ b/js/src/frontend/BytecodeEmitter.cpp
@@ -107,6 +107,7 @@ BytecodeEmitter::BytecodeEmitter(BytecodeEmitter *parent,
     hasSingletons(false),
     emittingForInit(false),
     emittingRunOnceLambda(false),
+    lazyRunOnceLambda(false),
     insideEval(insideEval),
     hasGlobalScope(hasGlobalScope),
     emitterMode(emitterMode)
@@ -2666,10 +2667,11 @@ frontend::EmitFunctionScript(ExclusiveContext *cx, BytecodeEmitter *bce, ParseNo
      * the script ends up running multiple times via foo.caller related
      * shenanigans.
      */
-    bool runOnce = bce->parent &&
-        bce->parent->emittingRunOnceLambda &&
+    bool runOnce =
+        bce->isRunOnceLambda() &&
         !funbox->argumentsHasLocalBinding() &&
-        !funbox->isGenerator();
+        !funbox->isGenerator() &&
+        !funbox->function()->name();
     if (runOnce) {
         bce->switchToProlog();
         if (Emit1(cx, bce, JSOP_RUNONCE) < 0)
@@ -4788,9 +4790,7 @@ EmitFunc(ExclusiveContext *cx, BytecodeEmitter *bce, ParseNode *pn)
             bce->script->compileAndGo &&
             fun->isInterpreted() &&
             (bce->checkSingletonContext() ||
-             (!bce->isInLoop() &&
-              bce->parent &&
-              bce->parent->emittingRunOnceLambda));
+             (!bce->isInLoop() && bce->isRunOnceLambda()));
         if (!JSFunction::setTypeForScriptedFunction(cx, fun, singleton))
             return false;
 
@@ -4801,6 +4801,8 @@ EmitFunc(ExclusiveContext *cx, BytecodeEmitter *bce, ParseNode *pn)
                     scope = bce->sc->asFunctionBox()->function();
                 fun->lazyScript()->setParent(scope, bce->script->sourceObject());
             }
+            if (bce->emittingRunOnceLambda)
+                fun->lazyScript()->setTreatAsRunOnce();
         } else {
             SharedContext *outersc = bce->sc;
 
diff --git a/js/src/frontend/BytecodeEmitter.h b/js/src/frontend/BytecodeEmitter.h
index 1711a47e548..b1dab973fde 100644
--- a/js/src/frontend/BytecodeEmitter.h
+++ b/js/src/frontend/BytecodeEmitter.h
@@ -124,6 +124,12 @@ struct BytecodeEmitter
 
     bool            emittingRunOnceLambda:1; /* true while emitting a lambda which is only
                                                 expected to run once. */
+    bool            lazyRunOnceLambda:1; /* true while lazily emitting a script for
+                                          * a lambda which is only expected to run once. */
+
+    bool isRunOnceLambda() {
+        return (parent && parent->emittingRunOnceLambda) || lazyRunOnceLambda;
+    }
 
     bool            insideEval:1;       /* True if compiling an eval-expression or a function
                                            nested inside an eval. */
diff --git a/js/src/jsscript.cpp b/js/src/jsscript.cpp
index d994bc3e323..255098796cc 100644
--- a/js/src/jsscript.cpp
+++ b/js/src/jsscript.cpp
@@ -2942,6 +2942,7 @@ LazyScript::LazyScript(JSFunction *fun, void *table, uint32_t numFreeVariables,
     directlyInsideEval_(false),
     usesArgumentsAndApply_(false),
     hasBeenCloned_(false),
+    treatAsRunOnce_(false),
     begin_(begin),
     end_(end),
     lineno_(lineno),
diff --git a/js/src/jsscript.h b/js/src/jsscript.h
index d1f98ed84e7..95f660dcfd9 100644
--- a/js/src/jsscript.h
+++ b/js/src/jsscript.h
@@ -1183,7 +1183,7 @@ class LazyScript : public gc::BarrieredCell<LazyScript>
     uint32_t version_ : 8;
 
     uint32_t numFreeVariables_ : 24;
-    uint32_t numInnerFunctions_ : 24;
+    uint32_t numInnerFunctions_ : 23;
 
     uint32_t generatorKindBits_:2;
 
@@ -1194,6 +1194,7 @@ class LazyScript : public gc::BarrieredCell<LazyScript>
     uint32_t directlyInsideEval_:1;
     uint32_t usesArgumentsAndApply_:1;
     uint32_t hasBeenCloned_:1;
+    uint32_t treatAsRunOnce_:1;
 
     // Source location for the script.
     uint32_t begin_;
@@ -1310,6 +1311,13 @@ class LazyScript : public gc::BarrieredCell<LazyScript>
         hasBeenCloned_ = true;
     }
 
+    bool treatAsRunOnce() const {
+        return treatAsRunOnce_;
+    }
+    void setTreatAsRunOnce() {
+        treatAsRunOnce_ = true;
+    }
+
     ScriptSource *source() const {
         return sourceObject()->source();
     }