To make the lime mayonnaise, mix the mayo and lime juice together, then set aside. Can be made the day before and chilled.
Put the mussels in a saucepan with a tight-fitting lid and pour over the wine. Cover the pan and place on a high heat for 1 min, then give it a shake and continue to cook for 2-3 mins until most of the mussels have opened. Tip the mussels into a colander set over a bowl to catch the stock. Freeze the stock for up to 2 months – it makes an intense base for a fish or seafood soup, risotto or sauce. When the mussels are cool enough to handle, remove the meat from the shells, discard the shells and dry the meat on kitchen paper. Can be prepared 1 day ahead and chilled.
Tip the flour, cayenne and baking powder into a bowl and season with a pinch of salt. Gradually whisk in about 150ml cold water until you have a thick batter.
Heat the oil in a deep-fat fryer or heavy-based saucepan to 180C. Dust the mussels in a scattering of flour, then tip them into the batter and gently mix until completely coated. Working in batches, use a spoon to drop the mussels into the hot oil and sizzle for 3-4 mins until crisp and golden. Use a slotted spoon to drain on kitchen paper and keep warm while you cook the next batch. Toast the buns, spread with the lime mayo and top with the lettuce and mussels. Drizzle over the chilli sauce and serve with the lime wedges for squeezing over.