check steam libary of the winner, select main game and you see which DLC's he owns. All before sending any key :)

There are only two ways to be sure one doesn't own one DLC, as I'm aware of:

• Adding the winner and simulate a gifting through Steam store. The store won't let you gift a game/DLC to someone who owns it already.
• You somehow ask the winner to add the DLC to his/her wishlist. One can't add any owned content to wishlist.

Either way is never really quick, though.

There's no other way to Goro, in my opinion ;D