Step 1 Heat the oven to 400 degrees.
Step 2 Place the lamb in a roasting dish and cook 50 minutes.
Step 3Remove the lamb from the oven to a large dish. Make 3 (5-inch) cuts down to the bone on each side, if using the shoulder, or 4 cuts to the bone through the meatiest part of the leg, and rub the cayenne and salt into the cuts. Let the meat sit in the dish 5 minutes and save the juices that drain.
Step 4Meanwhile, heat the grill to medium-high.
Step 5Grill the lamb and cook, turning once, until the meat at the bone is cooked medium-rare, 25 to 30 minutes, or until a meat thermometer registers 140 degrees. Remove from the grill and let sit 10 minutes.