If preparing in conjunction with the fire-roasted artichokes, the barbecue should be lit and then artichokes started when this dish is begun. If not, light the barbecue.
Clean and trim both racks of lamb and cut into 8 double chops. Chop the rosemary with salt. Rub the chops with the herbs and drizzle with 2 tablespoons of extra-virgin olive oil. Set aside.
In a 2 to 3-quart saucepan, heat the 3 remaining tablespoons olive oil over high heat. Before the oil begins to smoke, add the onion and cook until softened, about 7 to 9 minutes. Add the sugar and continue cooking until a dark brown caramel begins to form. Add the citrus juices, the zests, and simmer 5 minutes more. Add the fruit segments and simmer 2 more minutes, and remove from the heat.
Grill the lamb chops over the hot part of the grill 5 to 7 minutes per each side for medium rare. Remove the artichokes from the grill and arrange on a platter. Arrange the cooked lamb chops on the other end. Brush the chops with marjaram leaves dipped in citrus sauce. Garnish with parsley and serve immediately with Fire Roasted Artichokes.