Should you be able to enter a DLC giveaway if you don't own the game?

Supposedly it is not possible. It might be a sync issue or just a glitch with one or two particular games which has happened before and is a known issue with some titles. If I were you I would contact a moderator through the Support feature and ask them what the proper way to deal with that situation is, before handling those people the said DLC.

No. Why would you want to in the first place. You need the base game to use it.

sometimes you dont have the game but you also can enter.

During free weekends, everyone gets a time limited subscription of the game. Steamgifts cannot distinguish between that and an actual purchased subscription, so you could enter for giveaways for DLCs of the game. But that would be against the rules

You cannot technically hand them over the DLC anyway as Steam would not allow them to take it, right?

In cases such as this the winner should be re-rolled and those people warned if they are repeat offenders. But I don't know if that is possible.

If a gifter notices the winner of their giveaway won DLC without owning the base game, please create a support ticket and you may refuse to give them the DLC.

Happens all the time. Steam is weird like that.