When someone lies in court, the opponent has to be prepared to confront them with a prior inconsistent statement made under oath somewhere during cross examination. That is not the same as arguing with them.
Every month it seems someone appears in my office with a document someone has signed under oath, or declaration swearing the contents to be the truth “on pain of perjury” and declaring they have lied!
Truth is hard to find. One mans black is another mans white.
My Dad used to say that the reason we lawyers have jobs is one guy cannot see the other guys point of view. And that is why there are no trap doors or sudden death in civil or criminal law.