We've eaten at LTT twice with our peanut and tree nut allergic DD. We've done both lunch and dinner.
Dinner is famly style, you don't order off a menu. The dessert we were served was apple crisp, but DD couldn't have it. Instead, they brought her some vanilla ice cream. They even brought ice cream for DS, who doesn't have allergies but doesn't like apple crisp.
At lunch, you order off the menu. DD got the turkey dinner. The best part was that she could have the chocolate cake for dessert! She's already said that she wants to go back there since there are so few places where she can have dessert.