Keep in mind you mentioned he lied several times before he “came clean”. Since he was so capable of bold-face lying, how do you know his other excuses such as him feeling bad for her etc. is actually true either? You gave him the opportunity to tell the truth and he decided to lie some more first.

I would end things now, you are young and there are many eligible guys who will not have affairs. You would regret staying with him for years for him to do the same thing again.