1. Preheat grill to 350° to 400° (medium-high) heat. Stir together first 3 ingredients, 1 pressed garlic clove, and 1/2 tsp. salt. Cover and chill until ready to serve.
2. Gently combine lamb, next 4 ingredients, and remaining 2 pressed garlic cloves and 1 1/4 tsp. salt. Shape mixture into 6 (4-inch) patties.
3. Grill patties, covered with grill lid, 5 to 6 minutes on each side or to desired degree of doneness. Serve burgers on buns with yogurt sauce and desired toppings.