I agree with Rhinnonsmoon.

You have seen that his behavior is completely untrustworthy. He has cheated on you many times and clearly he isnt always honest with you either.

It seems like you do realize that your lying has had some effect possibly and you need to take that knowledge and learn. Learn that lying ruins the foundation of a realtionship. Be honest in your future relationships and dont lie to make it work because you ruin it when you lie.

Set your boundaries in the relationship clearly when it starts. Make sure you state your limits clearly. That for you cheating is not an option. Have a certain plan about the penalty within the relationship for cheating. Follow that plan and be true to yourself. If you dont follow through with your plan and you let your partner violate your limits you are sending a clear message that you have no self respect. If you dont have self respect no one else will respect you either. You end up being just a tool. Stand firm on your limits.

Good luck!