When a faction is eliminated (you can do this without capturing the lords, you can take every castle and town so that the enemy lords can not spawn, and then destroy the remaining lords) their lords become "Free Lords", they will then join one of the remaining factions. They can not do so if they are in prison. I've heard that They are suppose to join factions at random, but to my experience they would rather join a faction that they have not been much at war with.
You will not get money for them. They can escape. When they escape they will join one of the remaining factions. I'd suggest you let them rot, there is nothing else you can do. You can not free lords, but you can tweak their chance of escaping.
EDIT: If their King was not imprisoned he would vanish. So, when you defeat a faction all their lords remain, but the king (or khan) is removed from the game (unless, as said, he is in your prison).