I don't know about cheating, but he is definitely hiding something. If he lies this easy about the small stuff, when does he tell the truth? If you want to make this work, you need some counseling, but I think from your post, you believe that he is cheating. Remember, these two friends are just the ones that you KNOW about.
Christmas isn't the best time for a break up, but if you wait till after Christmas, New Years is around the corner....then Valentines Day, etc. You need to sort this out. Whether that is a long heart to heart discussion as to why he is constantly lying, and having caught him in these lies you are having a lot of trouble trusting him, or the fact that he did cheat, and he needs to move out.