Gently pat the lobster meat dry with paper towels to remove excess moisture. This ensures your filling won't become watery.
In a large bowl, combine the mayonnaise, lemon juice, diced celery, and chives.
Fold in the lobster meat carefully to avoid breaking it up too much. Season with salt and pepper to taste.
Cover the mixture and refrigerate for at least 30 minutes to allow flavors to meld.
Just before serving, heat a large skillet over medium heat.
Butter the outer sides of each split-top bun.
Toast the buns in the skillet until golden brown on both sides, about 2-3 minutes per side.
Fill each toasted bun with the chilled lobster mixture.
Serve immediately while the buns are still warm.