how to forgive? that is a hard one. to me, trust is everything and if you can't trust someone...where is the foundation of the relationship. I could never share a home with someone I didn't trust. and I believe there are somethings that are simply unforgivable in my book. things that "sorry" simply cant fix.
if he promises not to do it again, yet does time and time again. that is probably something that will never change. he will continue to do that over and over again. can you accept deceit as part of your relationship with him? do you know why he is doing whatever he is doing that he has to lie about? do you think he will ever stop?
I hate to see any marriage fail. have you tried going to counciling together?
you didn't say what he lies about, but if it is something that could cause you physical harm, put you in trouble with the law or cause your financial future to go down the drain - get away from him!