If your reason to want to work it out is that you still love this person, think about what self respect means. Get a little therapy. Take a little time. Think about how this person treated you by lying and cheating. Love is hard, and most of us at one time or another has loved the wrong person. But spending your life with a person that clearly does not love you back is a horrible thing to do to yourself. It's soul sickening.
Let's make this clear: You deserve to be loved. This person does not love you. No matter what they've said out of guilt or fear, they do not love you. Nuff said!