Is my ex keeping me as an option, or is this relationship over?

I was in a three-year relationship. About seven months ago, my girlfriend broke up with me because of a lie I told. The reason for the lie was that she didn't want me seeing the male friends I’d known for years; in other words, there wasn't another woman in my life—I had simply met up with my friends. After the breakup, I tried for three months to win her back. When that didn't work, I gave up, and some time later, I met someone new. This person came to the city where I live; we talked for a few days, but we never met up after that.
My girlfriend found out about this and asked me. At first, I said "no," but when she asked again, I decided to be honest and explained the situation clearly. We haven't been a couple for the last two months, yet we continue to call and see each other. However, she constantly tells me, "Nothing is going to happen between us; don't get your hopes up." One day she treats me very well, but the next, she ignores my calls and messages as if nothing happened. Then, a few days later, she’s the one calling and texting me.
Finally, unable to stand the uncertainty any longer, I asked, "What is your goal here?" She told me, "I don't consider a serious relationship with someone who lies to me, talks to someone else while talking to me, or leaves me to go be with another person; nor do I want to hang out with someone who does those things to me." But here’s the thing: I have no idea what she was doing or if there was anyone in her life during the time we were apart. On top of that, she still hasn't told her family that we broke up. What do you think her goal is?
Is my ex keeping me as an option, or is this relationship over?
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