It seems clear that right now she is not able to be completely candid with you at all times. I grant that this looks like a character flaw, but everybody on earth has character flaws. To me, the question is not whether she has a flaw, but how significant is this flaw in your relationship: does it outweigh outweigh the many good things you see in her and in the relationship?

Good scenario: She doesn't lie very often and you address her lying by, each time it happens, gently, nonjudgmentally calling her on it at the time (without by bringing up old stuff like the dic pic, never saying saying "You always lie", "You are an f-ing liar", etc. Just stick to the incident at hand) and having a mutually respectful discussion. With this approach you may gradually help her learn not to lie.

Bad scenario: She lies a lot, and it turns out the lies re about major, current things like she is seeing another guy, she keeps reaching out for abusive ex, etc. Plus, she refuses to discuss anything. In this scenario you come to realize that she doesn't really love you, regardless of what she says. You end the relationship.

The question is: how much are you willing to take a chance on experiencing a bad scenario in order to try to cultivate the good scenario?

I don't see this is a matter of right or wrong.To me, it just isn't clear right now. This is why it is a hard decision.

It sounds like you really want the relationship to work, that you really love the many good things you see. If you don't give the relationship every possible to chance to work, how will you feel when you look back and realize that you ended the relationship before giving it every possible chance?

And, on the other hand, if later on the bad scenario materializes and you are really hurt, how will you feel looking back and knowing that by giving it every possible chance you opened yourself to more hurt?

My suggestion is to weigh these two possible outcomes and see which path resonates more deeply with you, better fits who you are.