How do you punish your girlfriend for lying?

If you want to punish her, you don't love her. Punishment is a form of domination, not love. So if you don't trust her, you need to find out why. Move on, brother, you don't know what love is yet. She's not worth it, and you need to look inside yourself to find out why you want to be the boss of another human being. The path you're on now will lead to abuse, so stop and think now before you become a physical abuser.