1. Why in the world would you want to form a relationship with a man who is clearly not trustworthy? Are you kidding yourself? Do you really think that is all you deserve?
No, you should not get back to him. If he cheats, then lies about it, what other problems does he have?
2. An open relationship takes complete honesty (he doesn't have it), trust (you no longer have it), and an acceptance of the situation. Also, it doesn't work with people who have issues with jealousy. It's very difficult, because you have to really deal honestly with your own emotional issues, and trust your partner completely, before an open relationship will work. Not many people make it work because of this. They are in denial that they have issues, or they don't want to deal with them, or counseling is too expensive. Whatever.
I have read about people who make it work and they are very happy. I do not recommend it to everyone. And I do not recommend it for you.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
(Please note, we give the best advice we can based on the information given in a post. For better advice, please include the age of all romantic partners.)