1.In a medium bowl, combine the lobster meat, mayonnaise, celery, lemon juice, parsley, a pinch of salt, and some pepper. Mix well to coat the lobster with the mayonnaise. Chill.
2.Flatten the hot dog buns without splitting them apart. Generously butter the cut side and sprinkle with some salt. Heat a cast-iron over medium-high heat and place the buns in the pan buttered side down and toast until golden brown, 4 or 5 minutes.
3.Remove the buns to serving plates, toasted side up. Place a two lettuce leaves on top and spoon one fourth of the lobster salad on each sandwich. Pull up the sides and serve.