More than 50% of marriages result in divorce. The leading cause is lack of trust due to cheating and/or lying. It would be very difficult, even near impossible, to finish your life course with someone you don't trust. The only hope for resolving this is professional couples counseling. If your husband refuses to participate, it would be entirely appropriate to refuse intimacy and even refuse to share the bed.
What are the lies is he telling. There is a huge difference between no honey you don't look fat, umm your meatloaf is great & Honey I'm working late & you see him walking some chick into a hotel. We all lie all the time. What when why & how is he a liar.