Fill a large stockpot with salted water and bring to a rolling boil over high heat. Add the whole lobsters and cook for 12-15 minutes until shells turn bright red. Remove and let cool completely.

Once cooled, crack the lobster shells and extract all the meat from the claws, knuckles, and tail. Cut the meat into bite-sized chunks, roughly 1/2 to 3/4 inch pieces. Place in a bowl and refrigerate while preparing other ingredients.

In a mixing bowl, combine mayonnaise, fresh lemon juice, minced celery, and a pinch of salt and black pepper. Mix gently until well combined. Add the chilled lobster meat and fold gently to coat, being careful not to break up the chunks. Taste and adjust seasoning if needed.

Heat a large skillet over medium heat and add butter. Once melted and foaming, place the split-top buns cut-side down in the skillet. Toast for 2-3 minutes until golden brown and crispy.

Line each toasted bun with crisp lettuce leaves. Divide the lobster mixture evenly among the four buns, mounding generously. Garnish with additional lemon wedges and serve immediately while the buns are still warm.