Lightly butter the insides of the buns or rolls and line with lettuce leaves. Set aside.
In a medium bowl, stir together the mayonnaise, lime juice, hot pepper sauce, salt and pepper until well blended. Mix in the green onion and celery, then lightly mix in the lobster so it just gets coated without falling apart.
Stuff the lobster filling into the buns and sprinkle parsley, basil or tarragon lightly over the filling.
Cut the lobster in half lengthwise, and remove the meat from the claws and tail. Leave to one side. Remove any meat from the head and set aside. Cut the meat up into pieces and place back into the shell.
Melt the butter in a large skillet over medium heat. Add the shallot; cook and stir until tender. Mix in the fish stock, white wine and double cream. Bring to a boil, and cook until reduced by half. Mix in the mustard, lemon juice, parsley, salt and pepper.
Preheat your oven's broiler. Place the lobster halves on a broiling pan or baking sheet, and spoon the sauce over the lobster meat in the shell. Sprinkle Parmesan cheese over the top.
Broil for 3 to 4 minutes, just until golden brown. Serve immediately.
In a small frying pan place 1/4 cup chicken stock and the onion. Cook over a low heat for 5 to 7 minutes.
In a medium size pot over medium heat melt the butter. Slowly whisk in flour. Whisk until a creamy mixture is created.
Gradually pour in stock, whisking constantly. Whisk in milk, salt, onion, lobster meat, Worcestershire sauce and cayenne pepper. Heat until soup is almost boiling. Do not boil the soup as the milk will curdle when boiled.