diff --git a/parso/python/errors.py b/parso/python/errors.py
index 429f10a..2f7c497 100644
--- a/parso/python/errors.py
+++ b/parso/python/errors.py
@@ -939,6 +939,10 @@ class _CheckAssignmentRule(SyntaxRule):
                 assert trailer.type == 'trailer'
                 if trailer.children[0] == '(':
                     error = 'function call'
+                elif is_namedexpr and trailer.children[0] == '[':
+                    error = 'subscript'
+                elif is_namedexpr and trailer.children[0] == '.':
+                    error = 'attribute'
         elif type_ in ('testlist_star_expr', 'exprlist', 'testlist'):
             for child in node.children[::2]:
                 self._check_assignment(child, is_deletion, is_namedexpr)
@@ -1078,26 +1082,4 @@ class _NamedExprRule(_CheckAssignmentRule):
                           'comprehension iteration variable %r' % first.value
                 self.add_issue(namedexpr_test, message=message)
 
-        if first.type == 'lambdef':
-            # (lambda: x := 1)
-            self.add_issue(namedexpr_test, message='cannot use named assignment with lambda')
-        elif first.type == 'atom_expr':
-            for child in first.children:
-                if child.type != 'trailer':
-                    continue
-                first_child = child.children[0]
-                if first_child.type == 'operator':
-                    if first_child.value == '[':
-                        # (a[i] := x)
-                        message = 'cannot use named assignment with subscript'
-                        self.add_issue(namedexpr_test, message=message)
-                    elif first_child.value == '.':
-                        # (a.b := c)
-                        message = 'cannot use named assignment with attribute'
-                        self.add_issue(namedexpr_test, message=message)
-                    elif first_child.value == '(':
-                        # (a[i] := x)
-                        message = 'cannot use named assignment with function call'
-                        self.add_issue(namedexpr_test, message=message)
-        else:
-            self._check_assignment(first, is_namedexpr=True)
+        self._check_assignment(first, is_namedexpr=True)
diff --git a/test/failing_examples.py b/test/failing_examples.py
index be905e2..44b8194 100644
--- a/test/failing_examples.py
+++ b/test/failing_examples.py
@@ -325,8 +325,10 @@ if sys.version_info[:2] >= (3, 8):
     FAILING_EXAMPLES += [
         # Case 2
         '(lambda: x := 1)',
+        '((lambda: x) := 1)',
         # Case 3
         '(a[i] := x)',
+        '((a[i]) := x)',
         '(a(i) := x)',
         # Case 4
         '(a.b := c)',
@@ -341,4 +343,7 @@ if sys.version_info[:2] >= (3, 8):
         '[i+1 for i in (lambda: (j:= range(5)))()]',
         # Case 7
         'class Example:\n [(j := i) for i in range(5)]',
+        # Not in that issue
+        '(await a := x)',
+        '((await a) := x)',
     ]