Did the wife's divorce from her lying husband occur after he swore to divorce her if he lied about having another relationship, and then his lie became apparent?

Since the husband has lied, his divorce has taken effect according to the majority of scholars, and this is the fatwa-based opinion, contrary to Ibn Taymiyyah, who holds that a conditional divorce does not take effect if it was intended as a threat, and that it can be expiated by an oath. If it was the first or second divorce, he may take you back as long as you are within your iddah (waiting period). However, if it was the third divorce, then you are irrevocably separated from him (baynunah kubra), and you will not be lawful for him unless you marry another husband and he then divorces you or dies, and your iddah from him ends. You erred by asking for your divorce to be conditional on his lying. The correct approach is to advise him and live with him amicably. If that does not work, then an arbitrator from his family and an arbitrator from your family should intervene to reconcile between you.