In a bowl, gently mix ground beef, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Divide meat mixture into eight equal portions and shape each into a 4-inch round. Top each of four rounds with 2 slices of cheese. Lay another patty on top of each and press edges together to seal.
Lay burgers and onion slices on an oiled barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook burgers, turning once, until browned on both sides and done to your liking (cut to test), about 7 minutes total for medium-rare. Cook onions, also turning once, until browned on both sides, 7 to 8 minutes total. Remove from grill.
Lay buns, cut side down, on grill and cook until lightly toasted, 30 seconds to 1 minute.
Spread Sweet-and-Spicy Sauce on bun bottoms. Add lettuce, tomato, burger, onion, and Guacamole. Set bun tops in place. Serve with remaining Guacamole, sauce, and salt and pepper to add to taste.