TheFork users who ate in Luzern have said really good things about Olivo, GourmIndia Luzern and Restaurant Lumières. Maybe you should give them a try!
Some of the more popular Private Dining restaurants that offer private dining options in Luzern according to TheFork users include:
Olivo, with a 9.7 rating
GourmIndia Luzern, with a 9.5 rating
Restaurant Lumières, with a 8.9 rating
The moment you suggest that you throw your friend a surprise party, panic sets in. But don't worry, there are quite a few restaurants where you can rent out a dining room for special events. Bet you feel better already!