Fill a large stockpot with water, leaving room for the lobsters, and bring to a rolling boil. Salt generously, about 1 tablespoon per quart (15 ml per liter).
Using tongs, lower live lobsters in headfirst, cover, and boil for 8 to 10 minutes for lobsters around 1.5 lb (680 g) each, until shells turn bright red. Meat should reach 135 to 140°F (57 to 60°C). Skip this step if using pre-cooked meat.
Lift lobsters out with tongs and plunge into a large bowl of ice water to stop the cooking. Let cool for about 10 minutes until cold enough to handle comfortably.
Twist off claws, knuckles, and tail, then use crackers and shears to open the shells. Pull out all the meat, keeping pieces as large as possible, and discard any shell fragments.
Cut the meat into bite-size chunks, roughly 3/4 inch (2 cm), and keep it chilled. You should have about 1 lb (450 g) of picked meat.
In a medium glass bowl, stir together the mayonnaise, lemon juice, lemon zest, and Old Bay if using. Add the finely diced celery, chopped chives, and dill if using, then mix to combine.
Fold in the chilled lobster meat gently so the pieces stay intact and do not shred. Season with sea salt and black pepper, then taste and adjust with a little more salt or lemon if needed.
Keep the salad cold in the fridge while you toast the buns.
Spread softened butter over both flat outer sides of each split-top bun. Heat a cast iron griddle or skillet over medium heat until hot.
Place the buns on their buttered sides and toast for 1 to 2 minutes per side, until deep golden and crisp. Watch closely since butter can go from golden to burnt quickly. Let cool for a few seconds.
Open each bun gently and divide the cold lobster salad evenly among the four buns, mounding it slightly. Dust tops with a pinch of smoked paprika if using.
Serve right away with lemon wedges on the side. Dress the meat just before filling, never in advance, so the buns stay crisp and the salad stays cold.