For the lettuce sandwiches: Spread mayonnaise on 4 slices of bread. Cut the iceberg lettuce into 4 thick slices and place each on top of the mayonnaise. Spread more mayonnaise on top of each lettuce slice and season with lots of salt and pepper. Layer a few leaves of garden lettuce on top and finish each sandwich by topping it with the remaining slices of bread. Slice the sandwiches in half and serve with the lobster.
Serve the lobster immediately with the lemon butter and the lettuce sandwiches.