It seems you already know. You cannot change anyone or make them do anything they choose not to do. I do not think one just begins to lie, it typically is because they always have & you just either had no reason to pay attention to them, or they did not affect you at the time. Now that it does effect you, you see how trouble some it can be.
It is sad when one can do this. It is not just you he is lieing to, it is also lieing to himself and what he takes away from himself by doing so. You need to make sure you do not become a victim of his insecurities and allow him to drag you down until you cannot get out of that mess.
Each time he lies & believes he gets away with it, it only makes him more confident in doing so. It is not easy to live with and the choices you need to make are not easy choices, but for you & your children, you need to, in my opinion.
I lost my wife of 30 years, she was my life, I was so lost & life just was not something I looked fwd to. I then met this girl, that had all the right words at the right time, gave me reason to smile, laugh, & most of all, live for a bit without that pain that was eating inside of me. I finally thought I was going to move on in life & actually live again. Soon I realized this girl needed a note book to keep her stories straight. Some of the simplest things were lies, for no reason. I finally realized it was just who she was and she was not going to change. As well as knowing any change would be nothing more than better hiding of lies or being more careful.
And the sad thing is people like that believe everyone lies, it is normal for all to. If that is not who you are, that is hard to understand. Before long you try to justify why one may have to lie, try to overlook it, then they try to make it like it is you who are the confused one. The first time I caught myself saying I will simply record one of her stories and play it back when the truth comes out. As soon as i thouhgt about doing this, I realized she was giving me reason to play her games and or question myself. That was the day I decided it was time to end this relationship. I still to this day do not blame her, it is who she is, sad because she truly is a beautiful woman, inside & out, with exception of this. Something in her life gave her reason to live as this. She got me thru a time in my life, I don;t know how else I would have got thru. These are the things I choose to remember about her, the good things she did & offered. My only regret is, this part of her life that is one of lies & stories. But it is who she is & not for me to change, now or ever. To remain I would have to lessen who I was & am.
I have always believed a cheater will always cheat & believe all do. A lier will always lie & believe all do. A theif will always steal & believe everyone does. This is a chosen life style they choose. No other person will change them, for any reason. We are responsible for our life & the life of children we chose to have & be responsible for.
I am sorry you are dealing with this in your life, but for you & your children, you need to give serious thought to your future. Things parents say & do will effect children far more than most will believe. Everyone here can say kick him to the curb, talk to him, look the other way, ect ect, but we do not live in your life or world, nor should we tell you what to do, only offer our belief & or veiws.
I wish you & your children the very best