8 top-split hot dog buns (1 package), halved crosswise
Combine lobster, mayonnaise, lemon juice, chives, salt, and Old Bay, and cayenne if desired, in a small bowl.
Heat butter in a 12-inch skillet over medium-high heat. Working in batches, toast buns until golden brown, about 3 minutes per side, transferring to a paper-towel-lined plate as you work. Fill each bun with 1/4 cup lobster salad.