I suggest you ask your attorney to provide you with an accounting of time spent on your case and what he received in fees. It's possible that your mother missed a payment for some reason. That's the first step. Then have a conversation with him regarding why he withdrew. If you are not satisfied with the answer, then you can file a grievance with the bar association. Information is at wsba.org.
The answers to these questions may be different depending on your individual circumstance and should not be considered as legal advice or the establishment of an attorney-client relationship.
To answer the simpler top line question: No, an attorney is not allowed to lie to the court.
My answers to questions are for general purposes only and do not constitute legal advice or establish any attorney-client relationship.