Don't forget the IC Critical Flaw is simply something that reduces his influence on the Main Character. So it doesn't have to be something that hurts him -- it could even be something that helps him get what he wants. But something about his crude lack of class dulls his influence on Lawanda.
So far we don't have a lot defined about Lawanda and Clay's throughlines yet, but we know Lawanda is someone who likes to get people's permission (Unique Ability), and permits/acquiesces to her sister even when she shouldn't (Issue). Then look to your MC Solution illustration as to how she changes -- that's the direction that Clay's influence is pointing her: something that allows her to change and give consent to the martial arts practitioners.
EDIT: sorry I didn't make the 2nd paragraph above clear. The point of trying to explain what the direction of Clay's influence was, was to make it easier to picture how something could dull that influence. But you can ignore that ... anything that makes Lawanda annoyed, or able to ignore him, or able to dismiss him, or less likely to be physically present with him, ANYTHING at all like that will work.