Under the circumstances you would do better, in my opinion, to move on.
Your Girlfriend (GF), has deep seated issues that relate to her formidable years growing up, and her primary relationships during that time.
It takes more than a simple flip of the switch, so to speak, to fix this type of thing. It normally takes a significant emotional event, and follow up activities to work through the issues. A significant emotional event could be losing someone she really loves and cares about; and the follow up activities are therapeutic consultation with a relationship expert or psychotherapist or psychologist. (or similar).
If you continue in this relationship I expect that she will not be encouraged to change, and that at some level you have co-dependent type behaviors that enable her to continue in her behavior. People do not often like to hear that they may have behaviors that help the other person stay where they are,but it is a fact of life, in the realm of human behavior, that some personalities enable each other in different ways. In this situation, she habitually lies (or maybe even pathologically lies), and is unable to be faithful.
In my opinion, if you love yourself, and her, you will leave her. Tell her something like this:
You know how I feel about you; that I love you very much. However, I am not going to stand by in relationship with you and watch you go out with other guys; and I am not going to allow myself to be lied to. I am sorry, but I am no longer going to be in relationship with you.
AND mean it. Say it and mean it.
You will know if she is sincere about you if she gets the counseling she needs. That will show her sincerity. However you need to be prepared for a lengthy courtship AFTER therapy, if that is what she does, because permanent change is hard to detect. A minimum of year is needed, but in some people, you will not know if change of this type is truly permanent for up to 5 years.
If she loves you, truly, in stead of moving on to someone else to be her enabler, she will seek out the change and actions required for her to be with you. In the mean time, you should continue looking for a healthy person with whom to have a relationship. If she makes the changes, and you are still available, then perhaps you would be able to start over again together.
Look for a new partner who enhances your goodness and helps to make you a better person. You want that partner who will bring out the best in you. You want someone who does not have to be a project, who does not need fixing.