In our Hodges variant, anyone can go out at any time; if playing partners in a teammate setting, both players must go out in order for the round to end. One player going out is an advantage generally, for us. If you're out and your teammate isn't, you keep drawing when it's you're turn just the same as if you did have cards, so that there is a chance you do draw something you can't play. All teammates being out of discards or playable cards is what ends the round, for us, not just one person on a team going out.
Did you mean to ask whether it is OK to lay down? Laying down, is the term we use for setting the first book or set of books down that meet the round's required score to make cards playable between teammates. In that case, it is generally polite to ask if it is OK to lay down.