The lying and cheating, it just sucks, I have tried to explain to her to just be honest with me, that I'm ok with her doing other "things", that I just want to know. She still continues to lie.
Can we leave aside whether or not your gf is has mental health issues for a moment? Let's start from assuming this is just a normal relationship. Why is it ok for her to do other "things"? Is it because you have no self esteem? Is it because she's so beautiful that you think you can't do better so you're willing to put up with infidelity (also, see previous sentence)? Is it that the sex is so mind-blowing that you can put up with all the other BS so long as you can make that connection with her you've never made with someone else (see previous two sentences)?
Forgive my directness, but as I've seen countless times on this board now and heard in my own personal therapy, these types of relationships are very similar to substance abuse disorders, and we're the junkies. In my own personal life, I can't think of a single reason to reconcile with my wife, yet I want to. My wife is stunningly beautiful. And, when we first started dating, she love bombed the hell out of me in every conceivable way. But now, years after getting married, she has no job, few skills, no aspirations, no real redeeming qualities you'd want in a mate, and the love bombing stopped a LONG time ago. But, she's still beautiful. Things haven't been like they were when we got married for YEARS, yet there's a flicker of hope that with the right help and right medicine and right whatever we can go back to the way things used to be. Only, the way things used to be wasn't real, and there's definitely a pathology to my compulsion to fix or rescue our marriage (leaving our children aside for the moment).
There are beautiful, successful, loving, STABLE women out there you won't have to make core comprises with to attain their love and affection. My question is, why do you feel compelled to settle?