Does a triple divorce occur due to lying under oath on the Quran, knowing that the purpose of the lie was to preserve the wife's feelings?

You made your wife's triple divorce conditional on your lying to her about your relationship with another woman, and then you lied to her. According to the majority of scholars, your wife has been irrevocably divorced from you with a major divorce (baynunah kubra). She is not lawful for you unless she marries another man in a marriage of genuine desire, not a tahlil (pre-arranged temporary) marriage, and that husband consummates the marriage with her, then divorces her, and her waiting period (iddah) from him ends. It is best to refer to the Sharia court. Informing your wife about your unlawful relationship is not permissible. The correct approach is to conceal your sin if you fall into disobedience, based on the Messenger of Allah (peace be upon him) saying: "O people, it is time for you to cease violating the limits of Allah. Whoever commits any of these abominations should conceal himself with the concealment of Allah, for whoever reveals his affair to us, we will apply the Book of Allah against him."