I would give him another chance but I would make sure that he knows the lying is the issue, not that he has a woman friend at work and goes to her parties, etc.

If you are not formally connected, he still can do whatever he wants in his time and even if you were married, he could, technically, go to coworker parties, etc. We're going to a party of my husband's former coworkers tonight and he just happens to be taking me with him but it would not bother me if I were not to go because I'm sure of him and his attachment to me. So I would make sure that your issues aren't trying to limit him as to who he's allowed to see, etc. (that's all his choice, always, it's his life) but that you do not wish to be lied to (so you can make your own, informed choices of what you want to do with your life).