You are probably thinking of Rule 3.03(a)(5) of the Texas Disciplinary Rules of Professional Conduct, which states, in pertinent part: "A lawyer shall not knowingly . . . offer or use evidence that the lawyer knows to be false." You can find this at www.txethics.org. This is not a law, but a rule of professional conduct, the violation of which can give rise to disciplinary proceedings. Of course, the person who gives the false evidence is also guilty of perjury, which is a felony.
In a normal situation like this there is nothing to be done....however, if she was mentally or physically abused by this man the local violence shelter might...repeat...MIGHT...be willing to represent her and then ask for lawyer fees from the father.
i would have her call them and see what can be done...they can always reschedule the deposition....and to be honest I have never HEARD of a deposition of the other parent in a child custody case. It sounds to me like they are trying to fish for quotes like "has he ever harmed the child"...well no....Okay, no need to explain further.....has he always provided for you and the child while you were together....well not recently, NO I said while you were together...well yes.....
etc....they want sound bites. I would seek help soon.