Stir together lobster and mayonnaise. Stir in chives and tarragon (if desired), and lemon juice; season with salt and pepper. Refrigerate, covered, while preparing rolls, or up to 2 hours.
Heat a large heavy skillet or griddle over medium heat until hot. Lightly brush outside of buns with butter; transfer to skillet. Cook, turning once, until golden brown, about 1 1/2 minutes per side.
Spoon about 1/2 cup lobster mixture into each bun. Serve immediately.