Steam the lobster in 2 inches of boiling water until bright pink, 8 to 10 minutes. Immediately shock in an ice bath, and then remove the tail and claw meat. Chop and reserve.
Mix the lobster meat, tarragon, celery and lemon juice together in a medium bowl. Fold in the mayonnaise and season with salt and pepper.
Brush the outside of each roll with some butter and griddle or toast until golden brown. Fill each roll with the lobster salad and garnish with the chives. Serve immediately with lemon wedges on the side.