Preheat a grill or grill pan. Mix the salt, cayenne and black pepper and sprinkle evenly on both sides of the steak. Grill the steak, covered, for 5 to 7 minutes on each side for medium-rare. Transfer to a plate and squeeze the juice from each lime half over each side of the steak. Tent with foil and let rest for 10 minutes. Thinly slice the steak across the grain.
Meanwhile, toast the rolls on the grill. In a small bowl, combine the mayonnaise and chili powder. Spread the chili-mayonnaise on each roll bottom. Pile on the steak, avocado and lettuce; cover with the roll tops.