In a large pot, bring salted water to a boil. Deposit lobsters to cook them until they are bright red, about 10 minutes. Using tongs, transfer the cooked lobsters to the ice water bath for 2 minutes. Drain the lobsters. Twist off the lobster tails and claws. Remove the meat. Discard the intestinal vein that runs the length of the lobster tail.
Cut the lobster meat into 1/2-inch pieces. Using paper towels, pat the lobster meat dry.
Heat a large cast iron skillet over medium heat. Brush both sides of each hot dog bun with melted butter and toast until golden brown on each side.
Spread a layer of mayonnaise on both insides of a toasted hot dog roll. Fill with lobster meat.
