diff --git a/src/Expr.cc b/src/Expr.cc
index af0cdb22f3..817dd70418 100644
--- a/src/Expr.cc
+++ b/src/Expr.cc
@@ -4673,11 +4673,11 @@ LambdaExpr::LambdaExpr(FunctionIngredientsPtr arg_ing, IDPList arg_outer_ids, st
 	else
 		my_name = name;
 
-	// Install that in the global_scope
-	lambda_id = install_ID(my_name.c_str(), "", true, false);
+	// Install that in the current scope.
+	lambda_id = install_ID(my_name.c_str(), current_module.c_str(), true, false);
 
 	// Update lamb's name
-	primary_func->SetName(my_name.c_str());
+	primary_func->SetName(lambda_id->Name());
 
 	auto v = make_intrusive<FuncVal>(primary_func);
 	lambda_id->SetVal(std::move(v));
@@ -4800,6 +4800,17 @@ void LambdaExpr::BuildName()
 	ODesc d;
 	primary_func->Describe(&d);
 
+	if ( captures )
+		for ( auto& c : *captures )
+			{
+			if ( c.IsDeepCopy() )
+				d.AddSP("copy");
+
+			if ( c.Id() )
+				// c.Id() will be nil for some errors
+				c.Id()->Describe(&d);
+			}
+
 	for ( ;; )
 		{
 		hash128_t h;
@@ -4807,7 +4818,7 @@ void LambdaExpr::BuildName()
 
 		my_name = "lambda_<" + std::to_string(h[0]) + ">";
 		auto fullname = make_full_var_name(current_module.data(), my_name.data());
-		const auto& id = global_scope()->Find(fullname);
+		const auto& id = current_scope()->Find(fullname);
 
 		if ( id )
 			// Just try again to make a unique lambda name.
@@ -4873,6 +4884,9 @@ void LambdaExpr::ExprDescribe(ODesc* d) const
 			if ( &c != &(*captures)[0] )
 				d->AddSP(", ");
 
+			if ( c.IsDeepCopy() )
+				d->AddSP("copy");
+
 			d->Add(c.Id()->Name());
 			}
 
diff --git a/testing/btest/Baseline/language.closure-binding-errors/.stderr b/testing/btest/Baseline/language.closure-binding-errors/.stderr
index 45bda39df5..91e54506a5 100644
--- a/testing/btest/Baseline/language.closure-binding-errors/.stderr
+++ b/testing/btest/Baseline/language.closure-binding-errors/.stderr
@@ -1,9 +1,9 @@
 ### BTest baseline data generated by btest-diff. Do not edit. Use "btest -U/-u" to update. Requires BTest >= 0.63.
-error in <...>/closure-binding-errors.zeek, line 12: a is captured but not used inside lambda (function(){ print no a!})
+error in <...>/closure-binding-errors.zeek, line 12: a is captured but not used inside lambda (function()[a]{ print no a!})
 error in <...>/closure-binding-errors.zeek, line 13: no such local identifier: a2
-error in <...>/closure-binding-errors.zeek, line 14: b is used inside lambda but not captured (function(){ print b})
-error in <...>/closure-binding-errors.zeek, line 15: a is captured but not used inside lambda (function(){ print b})
-error in <...>/closure-binding-errors.zeek, line 16: b listed multiple times in capture (function(){ print b})
+error in <...>/closure-binding-errors.zeek, line 14: b is used inside lambda but not captured (function()[a]{ print b})
+error in <...>/closure-binding-errors.zeek, line 15: a is captured but not used inside lambda (function()[a,  b]{ print b})
+error in <...>/closure-binding-errors.zeek, line 16: b listed multiple times in capture (function()[b,  b]{ print b})
 error in <...>/closure-binding-errors.zeek, line 18: cannot specify global in capture: c
 error in <...>/closure-binding-errors.zeek, line 19: cannot specify type in capture: t
 error in <...>/closure-binding-errors.zeek, line 9 and <...>/closure-binding-errors.zeek, line 20: already defined (a)