Fill a large pot with about 2 inches of water. Add 1 tablespoon salt and bring to a boil. Add the lobsters, cover and cook until the shells are bright red, about 10 minutes. Remove to a colander using tongs, then rinse under cold water to cool slightly.
Remove the meat from each lobster: Twist off the claws and tail. Remove the flippers at the end of the tail and insert your thumb to force out the meat. Crack the claws with the flat side of a knife or a lobster cracker; remove the meat. Roughly chop the lobster meat, transfer to a bowl and refrigerate about 15 minutes.
Meanwhile, preheat the oven to 400 degrees F. Lay the bacon on a foil-lined baking sheet and bake until browned and crisp, about 15 minutes; drain on paper towels. Combine the mayonnaise, chopped celery, basil and lemon juice in a large bowl; set aside.
Melt the butter in a large skillet over medium heat; add the buns and toast about 2 minutes per side. Spread about 1 tablespoon of the herbed mayonnaise in each roll. Stir the lobster meat into the remaining mayonnaise and season with salt and pepper. Fill each roll with a lettuce leaf, 1 slice of bacon, some lobster salad and a few tomato slices. Sprinkle with the celery leaves and chives. Crumble the remaining bacon slice and sprinkle on top.