Although we just heard him be sworn in here at the beginning of the episode, and he is under oath, perjury is a very different thing in civil cases than it is in criminal cases. In civil cases, there's no formal penalty for lying in a deposition, which Alex absolutely does multiple times in this three-hour session that he sits for.

Punishing him for perjury in a civil case would require winning the case and then after the fact having your lawyer file new criminal charges for the perjury charge. The best the prosecution could really hope for within this case is to demonstrate that Alex is being evasive or outright deceitful and then show evidence to illustrate that during the actual trial and cross-examination.