Lying is definitely the biggest problem in all relationships. The problem is people aren't as sensitive to how important the truth is between the people closest to us. It is too often taken for granted in how easy it is to lie and how easy people forgive and forget the lies.

If you want to keep the relationship it is going to be important to find out why she thought she needed to lie in the first place. Why does she want to undermine the relationship with the lies? Why does she not care about ruining your relationship with her? I don't mean that you should ask her these questions because you will get a superficial answer that is followed by some bullshit apology.

There is a reason she lied. It has to do with you or has to do with her. Do you make her feel guilty to having or keeping relationship outside of yours? Do you have any ideas what about you she feels the need to lie? For example, why did she say 'it wouldn't happen again' when excusing herself for talking to her old boyfriend as apposed to sharing with you the content of the conversation?

The things about her that might cause her to lie is past relationships and she is a consummate liar from the culture of her upbringing.

These are very broad terms so let me know which direction you want to go based on your perspective.