I'm going to lock my ex-boyfriend out of our house
Why are you going to lock him out?
He slept with some girl in our apartment while I was working late at the office.
This sounds complicated but locking him out is really disrespectful. It is not good to disrespect your roommate.
Don't take his side fag. He knows he shouldn't bring other girls to our house.
His behavior was disrespectful and unacceptable, but locking him isn't a viable option if he owns part of the house. If you were able to still cohabitate after breaking up, then I think having a conversation about the rules shouldn't be an issue and would be a much better way to go about it. If you have the legal standing, you could evict him.