Combine ground beef and Worcestershire sauce in medium bowl, mixing lightly but thoroughly. Shape into twelve 1/2-inch thick mini patties. Set aside.
Place pineapple slices on rack in broiler pan; brush with sauce. Place pan in oven so surface of pineapple is 3 to 4 inches from heat. Broil 4 minutes, turning once and brushing with sauce. Remove pineapple, keep warm.
Place patties on rack in broiler pan so surface of beef is 3 to 4 inches from heat. Broil 7 to 8 minutes for medium (160°F) doneness, until beef is not pink in center and juices show no pink color, turning once and brushing burgers with remaining sauce after turning.
Cut each pineapple slice into thirds. Line bottom of each roll with lettuce, top with burger, then with pineapple piece. Close sandwiches. Makes 4 servings.