Lying while swearing on my kids life

Just have to vent because i am pissed! So my ex (baby daddy) got caught cheating on his girlfriend and she came running to me about it. None of my business but ive been there with him before so i talked to her about it. Well come to find out he has been swearing on our daughters life that he wont cheat on her again...well...my ex is also a pathalogical liar, literally. He doesnt think twice about it because he is the kind who honestly believes his lies. He used to say the same thing to me while i was pregnant and he was constantly ceating on me and i promise he will do it again to her if she stays. I dont care what goes on in his personal life but i do care that he is swearing on our daughters life while he is lying 😡