To chop the duck breast, place in a food processor and pulse until meat chopped into pieces roughly the size of corn kernels. You can also use a sharp knife or meat grinder.
In a bowl, combine first 8 ingredients and mix well. Form into 4 large patties.
Place on a well-lubricated medium-hot barbecue grill and cook to desired doneness. Top with cheese and arrange in buns with lettuce and tomato. Combine mayonnaise, DU sauce and lime juice. Drizzle mixture over burger.