Trust, once broken, is hard to attain again. You must feel like she will no longer break your trust, if you are to trust her. Some of this is on her, some on you.
When we lie repeatedly and blame others, what we are typically doing is trying to justify our actions. Her blaming you is probably (based on my experience and study) her way of trying to justify her need to lie.
Chronic liars typically lie without realizing they are lying at the time, or they lie and feel like they cannot help it. Dependent upon the individual. Lying is often a way to hide from something. Usually negative self image. My guess without knowing more is that she probably has low self worth. Not to be mistaken for low self esteem. Self worth is far more notorious as it is subconscious and harder to detect on our own and usually from trauma.
The nature of the lies is important. Does she take a bite off the cheese block and then say it was you? Does she forget to do things and say you're to blame?
Does she cheat and say it's your fault? All of these issues have different driving forces. Some simple, some, not so much. In all cases, there is probably a deeper insecurity behind it.
If you want to be able to trust her, she probably has to stop lying. This is not something you can control. But you can influence it. If what she is lying about is also a problem (such as cheating), the two of you will have to find a way to both be happy. Talking it out to get to the source of th sincerely, without malice or frustration, and it and not giving up on her while not accepting e problem is very important if there is to be trust. She may not even be aware of why she behaves the way she does. When we talk about this kind of problem we need to be careful to let go of blame. If we talk to those we love with blame in our own voice, it simply compounds the issue. She most likely will feel guilt, and react to that guilt by blaming you. When we let go of blame and avoid "you" statements, it opens the door to thinking about her actions without feeling like a terrible person.
Her needs for certain feelings may not be met. She will need to communicate her needs to you, and you will need to help fulfil them. Again, you can only do your part. If she is not open to change, she will never change. I am confident that you can find the proper way to influence her to want to change. That means being very patient with her and relentless in finding a way. Study of NLP is the most efficient method I know of.