I'd stop seeing them and find someone that wants only me. You are responsible for your own happiness. You're entitled to have your own "deal breakers". In a situation such as this the person has either lied to you directly or by omission. A relationship which is not based upon HONESTY is not a real relationship! Without honesty there can be no TRUST. Why would anyone choose to continue to be emotionally invested with a liar and cheater? In the words of Whitney Houston, "The Greatest Love of All is Learning to Love Yourself" People who love themselves don't settle for scraps!
One man's opinion!