Preheat broiler. Put crabmeat in a bowl and add 1 tbsp. lime juice and toss to combine. In a small bowl, whisk together remaining 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 a 1/2-cup measuring cup. Holding toast on top of mixture in cup, invert crab onto the toast and set on an ungreased baking sheet. Repeat procedure with remaining crab mixture and toast and sprinkle 1 tbsp. Parmesan over each sandwich. Broil sandwiches about 3 inches from heat until cheese is melted and golden, 1 to 2 minutes.