TheFork users who ate in Lille have said really good things about Indian House, Chiquita Bacana and La Taverne Flamande. Maybe you should give them a try!
Some of the more popular Christmas and New Year restaurants where you can go with your pets in Lille according to TheFork users include:
Indian House, with a 9.4 rating
Chiquita Bacana, with a 9.4 rating
L'Express, with a 8.8 rating