If using live lobsters, steam them until the meat reaches an internal temperature of 135°F (57°C). Alternatively, use freshly cooked lobster meat.
Allow the lobster to cool until easy to handle.
Remove all the meat from the tails, claws, and knuckles.
Cut the lobster into bite-sized pieces, approximately ½ to 1 inch.
Place the lobster meat into a large bowl and gently toss with the mayonnaise until lightly coated.
Refrigerate for at least 1 hour to chill and allow any excess moisture to drain.
Add the diced celery and chopped chives.
Season with lemon juice, kosher salt, and freshly ground black pepper to taste.
Heat a large skillet over medium-low heat.
Melt 1 tablespoon of butter and toast the split-top buns on both sides until golden brown, adding more butter as needed.
Fill each toasted bun generously with the chilled lobster mixture.
Serve the Classic New England Lobster Rolls immediately with pickles, potato chips, lemon wedges, or your favorite summer side dishes.