Mix together the tomato sauce, pineapple juice, chili sauce, molasses and lemon juice to make the bbq sauce.
In a bowl, mix together beef, onions, bread crumbs, egg, parsley, garlic, salt and pepper.
Pour 1/3 of the bbq sauce over the meat mixture and blend together.
Shape the meat into 4 patties, about 3/4 inch thick.
Grill the patties on the grill or in the broiler.
Brush the patties with the remaining sauce and cook 5-10 minutes on each side until cooked to desired taste.
Place Pineapple slices on grill last 5 minutes. Turning the slices once.
While the burgers are cooking spread some bbq sauce on both bun halves. Place the lettuce, tomato and cheese on one side of the bun.
Place the grilled burger and pineapple slice on top of the cheese slice on the burger bun.
The heat of the burger will melt the cheese. Serve hot.