What is the ruling on a husband swearing falsely to his wife to avoid divorce, knowing that he has repented from previous unlawful relationships?

You should improve your relationship with your wife and make her feel her worth so that she forgets the situation. You must completely ignore the girl and not tell anyone what happened, because Allah is "Modest and Concealing, loves modesty and concealment," and to avoid severing ties of kinship or separating the spouses. Strive to indirectly remind the girl about modesty and warn her against falling into sin. Lying to your wife and denying what the girl said is permissible if it is to achieve a praiseworthy objective, such as maintaining a good marital relationship. The evidence for this is the noble Hadith (definition): "He is not a liar who reconciles between people, conveying good or saying good," which includes: "a man's conversation with his wife, and a wife's conversation with her husband." As for the false oath, it should have been avoided, but since it occurred, you must repent and seek forgiveness. Imam Shafi'i holds that expiation is obligatory for it.