Remove the meat from the lobsters, chopping any large chunks into bite-size pieces. In a bowl, combine the lobster meat, mayonnaise, lemon juice, celery, parsley, and salt and pepper to taste.
Brush cut sides of the rolls with melted butter and fill with the lobster salad.
Place lobster salad in refrigerator for 5 to 10 minutes. This allows the salad to absorb the flavorings.