I am sorry you are hurting.
I've always said Don't cheat on me and Don't lie to me - all else can be discussed. Especially since a large part of the reasons our first relationship ended was his lying to me about an encounter with one of my best friends and her husband while I was out of town.
If that is your hard limit? There it is then. It's on you to decide if you are going to enforce it by breaking up or not. He's a repeat offender.
I began to feel disrespected and disregarded as they seemed to become carried away with NRE and began to do some things, like PDA, that we all had agreed weren't going to take place.
It does not excuse the betrayal -- lies and such. Even if you break up with him for crossing a hard limit.
But for future reference, and esp since you have another lover -- in your relationships eventually the other
tier in the polymath will need expression.
When WOULD they be allowed to express these things? Was that covered?
Here's a thread that sort of goes there.