Combine first 3 ingredients in a food processor; pulse until finely chopped. Add mayonnaise and next 3 ingredients; pulse until blended. Add shrimp; pulse until coarsely chopped. Stir in 2 cups breadcrumbs.
Shape soft mixture into 12 patties. Coat patties with remaining breadcrumbs.
Place a large, lightly oiled nonstick skillet over medium-high heat. Cook patties, in batches, 3 to 4 minutes on each side or until lightly browned. Serve with Lime Sauce.