Place lamb, fat-side up, on a cutting board; score the surface 1/4-inch deep in a crosshatch pattern and poke all over with a knife about 2 inches deep on both sides.

Combine salt, chili powder, black pepper, ancho chile, chipotle, oregano, cinnamon, and garlic powder in a large bowl. Add juices of orange, lemon, and lime, then whisk thoroughly.

Place lamb into the bowl with the marinade, coating it completely. Refrigerate uncovered for 24 to 48 hours, turning at least once halfway through.

Preheat the oven to 475°F (245°C).

Remove rack from roasting pan and scatter onions into the bottom. Replace the rack.

Toss potatoes, carrots, olive oil, minced garlic, and salt in a bowl until evenly coated. Arrange them around the lamb on the rack. Pour remaining marinade liquid and chicken stock into the bottom of the pan.

Place lamb in the preheated oven and immediately reduce temperature to 300°F (150°C). Roast for approximately 3 hours, or until the internal temperature reaches 135°F (57°C) for medium doneness.

Remove lamb from oven, cover loosely with foil, and let rest for 30 minutes before slicing.