OP, big hugs. If you can terminate, do so. If not, you will be a survivor and just focus on the baby. My advice would be like everyone else's, leave him.
But! I am with a similar person myself. And I struggle to leave the relationship. I know it is hard. I just tell myself, I will gather all my strength and leave. But I am still with him. I've been with my boyfriend for 1.5 years. I am divorced and got children, like you. I see lies flying out of his mouth left and right, without a second thought. I know that's not right but I was hopeful he is at least honest with me.
Recently, he's broken my trust with something fundamental. Now I know, he has been dishonest with me too.
He is still the same loving, kind, caring man, lots of attention, affection, good for my DC. Yet, he seems to be in denial of what he's done to me. I think they even lie to themselves.
I've lost my faith in men. I am so low, I think there aren't any good men, so why even bother dumping my bf and looking for another one. Maybe they all lie. That's not a good place to be.