Thank you for sharing your painful story with us. There isn't much I can add to the sage advice you've already been provided. Your relationship..like this man's sobriety..has derailed. As cold as this may sound to you...the most loving thing you can do for yourself, your child and this man is be prepared to sever this relationship. If you stay, you are tolerating both is lies and his drinking. You have to save yourself so that he has the room, space to save himself. He needs to face consequences of his actions. He is a grown man with the right of choice. You start being his mommy now...you always will be.
I had to be abandoned in my own rubble before I sobered up. I sobered up for the same reason I drank ...pain. It is when the pain of consequence outweighs its benefit that we are most likely to make a change.