In a bowl, add ground beef, egg, onion, bread crumbs, Worcestershire, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Mix well.
Divide mixture into four equal portions and shape each into a patty about 4 inches wide.
Lay burgers 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 no longer pink inside, 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 mayonnaise and ketchup on bun bottoms. Add lettuce, tomato, burger, onion, and salt and pepper to taste. Set bun tops in place.