Heat butter and olive oil in a large skillet over medium-low heat until the butter is melted. Add the onions and cook, stirring occasionally, until the onions are very soft and caramelized, about 30 minutes.

In a mixing bowl, combine the ground beef, Tamari Lite, garlic, pepper, and sugar. Mix to combine and let sit 15 minutes. Divide the mixture into 4 equal portions and shape into patties. Cook in a skillet or on a grill 3 minutes per side for medium. Serve on a lettuce leaf topped with a quarter of the onions.