Well, if you're very sure that you're boyfriend is actually lying to you, then prove that he is lying to you, and if he still doesn't admit it, then just leave him, and tell him it's over until he starts telling the truth. :)
Sorry if this doesn't help, this is just what I would do if I were a girl and in this situation.
Sorry if this doesn't help, this is just what I would do if I were a girl and in this situation.