Preheat barbeque or grill, then place artichokes on grill.
Clean and trim racks of lamb and cut into 8 double chops. Sprinkle chops with rosemary and brush with 2 tablespoons olive oil and set aside.
In a 2 to 3 quart sauce pan, heat 3 tablespoons olive oil over high heat. Add onion and cook until softened, about 7 to 9 minutes. Add sugar and cook until dark brown caramel begins to form. Add juices and zests and vinegar and simmer 5 minutes. Add fruit segments, simmer 2 minutes more and remove from heat.
Grill lamb chops over hot part of grill 5 to 7 minutes per side for medium rare. Remove artichokes from grill and arrange on platter. Arrange lamb chops at other end, drizzle with citrus sauce and garnish with parsley.