Most of the time, a cheater is always a cheater.
If you wish to give him another chance (and it's up to you), start over from the beginning.
He has to rebuild that trust from the ground up. It'll be very hard to not suspect him each time he's late. Each time he gets a strange phone call.
Once someone breaks this kind of trust, it's hard to trust them again.
But if you believe it was a one time mistake, go slow and start over.
If you think this was a long time affair where he lied to you constantly, then dump him. Guys who lie like that and are good at it are dogs.