Clients lie every day to us lawyers and to the courts. Sometimes it's an outright lie. Sometimes it's a lie of omission.
Sometimes they know it's a lie. Often it's just their version of the truth (shaded so that it sounds good to their ears).
If I feel that someone is deliberately misleading me, making it impossible for me to work for them, I "fire" them.
If someone sees things differently from the way the ex sees it, so be it. The court usually knows that the truth is somewhere in the middle.
FYI, lawyers are bound by the rules of ethics NOT to present testimony or evidence to a court that they know is false.
Does this answer your question?