Hi, Bickle.
I don't think it is necessary to bring the family to identify lies or fact-check in order to treat the pathology itself. I would even go further and say that in psychotherapy it actually doesn't matter if what a person is saying is the truth or a lie, because what is going to happen there is finding out what is the purpose of what the person is saying, the words they choose and the meaning of the stories they tell...
I found an article explaining how treatment for pathological lying works ("What to Do When Your Client is a Pathological Liar"), and I thought it could help you, but since I'm a new member, they won't let me share it
Just Google it if you are interested.
Best regards!