Stir mayonnaise, lime juice, Dijon mustard, sugar, and hot pepper sauce together in a bowl until smooth; season with salt and pepper.
Cover bowl with plastic wrap and refrigerate mustard sauce for at least 2 hours.
Mix beer, lemon juice, seafood seasoning, hot pepper sauce, garlic, cayenne pepper, and black pepper together in a saucepan; bring to a boil and add shrimp. Cook shrimp just until they are bright pink on the outside and the meat is no longer transparent in the center, about 2 minutes; drain immediately.
