In a large pot on high heat, bring 8 quarts of water to a rolling boil. Place lobsters in the water and allow them to cook for several minutes. When they float to the top, they are ready. Using tongs, remove them from the pot and cool under cold water. (Alternatively your seafood market or supermarket seafood counter may steam the lobsters free of charge–that’s what I did!).
Remove all the meat from the tails, knuckles, and claws and chop them into bite-size pieces. (I like to keep the tips of the claw meat intact for visual appeal.) Transfer the meat to a bowl and mix in the mayonnaise, lemon juice, celery, salt, pepper, and sugar.
Lightly butter the inside of the potato rolls and place them facedown in a frying pan on medium heat. Cook for 2 to 3 minutes or until they brown, taking care not to burn them.
Line each roll with a bed of shredded lettuce and then add a healthy scoop of the lobster salad.