I think you meant you want Luke back? If so I have to feel that it wouldn't be right. Especially if he knows everything that went on between you and Tim.
Speaking from my own experience of getting back with an ex after being with other people, there's always the elephant in the room. As soon as an argument arises, boom, there it is. With us at least, we couldn't get passed it and ended up miserable for a few more months before ending it for the second time.
This is just my personal POV. If you want him back, maybe ask to meet up with him, open up to him about how you feel, what you've done. If he's willing to accept that and wants you back too, then great. If not then at least you know where you stand don't hate yourself though, we all do things we later regret. Just put it down as a bad experience, one to learn from.