Is obedience to a mother afflicted with OCD (obsessive-compulsive disorder) related to cleanliness obligatory in her commands that might lead to extravagance, and is it permissible to lie to her or swear by Allah falsely to avoid harm?

First, you must advise your mother about the danger of succumbing to whispers (waswas), and that their cure lies in turning away from them and ignoring them. There is no blame upon you for not obeying her, even if you were to lie to her—giving the impression that her wish was fulfilled—so that she would not become angry. However, it is better to use allusive speech (ma'arid) to avoid lying.