Preheat broiler. Put crab meat in a bowl and add 1 tablespoon lime juice and toss to combine. In a small bowl, whisk together remaining tablespoon lime juice, mayonnaise, and mustard until smooth. Pour sauce over crab and toss to coat. Season crab mixture with salt and pepper and chill, covered, for 30 minutes. Lightly toast bread. Lightly butter toast. Spoon one fourth crab mixture into 1/2 cup measure. Holding toast on top of mixture in measure, invert crab onto the toast an set on an ungreased baking sheet. Repeat procedure with remaining crab mixture and toast and sprinkle 1 tablespoon Parmesan over each sandwich. Broil sandwiches about 3 inches from heat until cheese is melted and golden, 1 to 2 minutes.
» Serves 4.