Black lion Gemstore Gift Bug
You need to file a ticket with support to get this addressed.
Is your in-game mail full?
If you have deleted all your mail, and picked up all Gold and items from the Trading Post, waited an hour or two, and still no mail from the Gem Store (can one gift keys?), your friend (as they are the one that made the purchase) would need to contact the CS Team via the ‘Support’ link above/below and ‘Submit a Ticket’ for assistance.
Good luck.