Prepare the barbecue and the fire-roasted artichokes according to their respective recipes.

Clean and trim the racks of lamb, then cut into 8 double chops.

Sprinkle the lamb chops with finely chopped fresh rosemary.

Brush the chops with 2 tablespoons of virgin olive oil and set aside to marinate.

In a 2- to 3-quart saucepan, heat 3 tablespoons of virgin olive oil over high heat.

Add the sliced red onion to the saucepan and cook until softened, approximately 7 to 9 minutes.

Add the sugar to the softened onions and cook until a dark-brown caramel begins to form.

Pour in the juices and zests of the oranges, lemons, and limes, along with the red wine vinegar.

Simmer the citrus mixture for 5 minutes to allow the flavors to meld and the sauce to reduce slightly.

Gently fold in the orange, lemon, and lime segments.

Continue to simmer for 2 minutes more, then remove the sauce from the heat and set aside.

Grill the lamb chops over the hottest part of the grill for 5 to 7 minutes per side for medium-rare doneness.

Remove the fire-roasted artichokes from the grill.

Arrange the artichokes on a serving platter.

Place the grilled lamb chops at the opposite end of the platter.

Drizzle the lamb chops with the prepared citrus sauce.

Garnish the platter generously with finely chopped Italian parsley and serve immediately.