I would prefer it if all characters were being forced into the arena as it would give the group a sense of a common goal, that being survival. However I won't force you to be forced into the arena, we could say that you owed the lanista a debt which you couldn't pay so he struck a deal with you. Or whatever other reason you come up with. Just run it by me beforehand. I would be interested to know though.

EDIT: Oh, and don't feel restricted by the examples I've put up. Those are just that, examples.