The other thing to keep in mind is to see things as they are versus seeing them as you would like to believe. If you just recently started dating her and she's already lying and cheating, that's probably not a good sign right? Why would you think that would get better?
One approach you may want to consider is setting boundaries and preparing yourself mentally to be ready to enforce them without compromise -- i.e. if you lie to me I cannot be with you. That way it's explicitly up to her to decide to either act the way she needs to for you to stay engaged, or she should not expect you to be around.
Accuray
Agree with Accuray, 100%. ^^^
Brian, I have a ton of male friends who are divorced. I have been nothing short of STUNNED by how many (seemingly quality) women they attract, and what constitutes a "good catch."
You will do just fine, trust me. This is no time to compromise your integrity and beliefs.