Heat butter and olive oil in a large sauté pan. Add onions and pinch of salt. Cook for 5 minutes over medium-high heat then reduce heat medium and cook an additional 15 minutes or until the onions are soft and caramelized.
While onions are cooking, place lamb, shallot, garlic, thyme, salt and pepper in a mixing bowl. Gently mix together with hands or a fork, being careful not to compress the meat. Evenly divide the mixture into six patties.
Place patties on a hot, oiled grill and cook for 4 minutes. Flip and cook an addition 2 minutes or until desired doneness. Place on buns. Add 1 teaspoon of rhubarb ketchup on each burger and top with caramelized onions.