Heat a grill to high (450° to 550°). Meanwhile, combine mayonnaise, rosemary, and lemon juice; chill until using. Season salmon all over with salt and redfish rub.
Put onions and olive oil in a 10-in. cast-iron or other ovenproof skillet. Grill, covered, stirring often, until onions are caramelized, about 20 minutes. Remove skillet from grill and set aside.
Grill bread cut side down until toasted, about 45 seconds; transfer to a cutting board. Oil grill with tongs and paper towels. Set fish skinned side up on cooking grate and grill, covered, until grill marks appear and fish firms up enough to release easily from grate, about 3 minutes. Using 2 wide spatulas, turn fish over and grill until barely cooked through, 1 to 2 minutes more. Transfer fish to board.
Spread cut sides of bread with seasoned mayo. Stack lettuce, then tomato slices, fish, and onions inside sandwiches. Use long toothpicks to skewer each sandwich closed if you like and cut them in half.
* Buy Market Grill’s rub, called Blackened Redfish Seasoning, at marketspice.com. Or try our Test Kitchen hack: In a spice grinder, whirl 2 tbsp. paprika; 2 tsp. dried marjoram; 1/2 tsp. each onion powder, garlic powder, and freshly ground pepper; and 1/4 tsp. each cayenne and celery seed.