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 mean into 1/2-inch pieces.
Using paper towels, pat the lobster meat dry. Position a strainer over a large bowl. Place the lobster meat in the strainer, and refrigerate at least 1 hour.
In a large mixing bowl, toss the lobster meat and mayonnaise. Season with salt and pepper, to taste. Using a flexible rubber spatula, fold in celery, lemon juice and cayenne until thoroughly combined.
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.
Fill each toasted hot dog roll with lettuce and the lobster mix.
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