Mix ground beef, 1 can tomato sauce, egg, salt, and pepper in a bowl until combined. Form 6 patties and top each with an onion slice.
Heat oil in a large skillet over medium-high heat. Place burgers in the skillet, onion-side down, and brown for 3 to 5 minutes. Turn burgers and drain any grease. Top each burger with a lemon slice.
Combine remaining tomato sauce, Worcestershire sauce, sugar, chili powder, and mustard; pour over burgers. Cover and simmer until burgers are cooked through and sauce has thickened, at least 1 hour.