My girlfriend lied and is cheating on me?

[Ivy]

Sounds to me like your relationship problems go deeper than this one mishap. Maybe she's looking for a way out, and wants to make you look like the bad guy, or even make herself look bad so you'll dump her. The fact that she lied to you and went out with a friend instead is a big red flag. In a relationship, you should have enough honesty to just say 'Hey, I just want to hang out with my friend tonight'.
Bringing social media sites (IE Facebook, Twitter etc..) into your fight is a quick way to ruin a relationship. If you feel like your relationship is in trouble, pull her aside. Take a few hours to sit down alone with each other, no phones, no Twitter, and no outside opinions. You two really need to sit down and talk about your relationship. Lay all your cards on the table and figure out where you both stand.
For what it's worth, I don't think she's cheating on you.