Mix ground beef, egg, onion, bread crumbs, garlic, salt and pepper. Divide the mixture into four equal portions and shape each into a patty.
Lay burgers on high heat on a gas grill and then close the lid on the grill. Cook the burgers, until brown on both sides and no longer pink inside (cut to check) for about 7 to 8 minutes then remove them from the grill.
Lay the buns with the cut side down, on the grill, and cook until lightly toasted.
Spread the mayonnaise and ketchup on the bun bottoms. Add lettuce, tomato slices, burger, onion slices, and salt and pepper to taste. Set bun tops in place. Serve!