Rub the marinade evenly over the lamb, coating all sides. Cover and refrigerate for at least a few hours or overnight for best flavor.
Remove the lamb from the refrigerator and let it sit at room temperature for about 1 hour before cooking.
Preheat the smoker to 225°F.
Place the lamb directly on the smoker grates and cook until it reaches your desired internal temperature (about 125°F for medium-rare, 135°F for medium).
Remove the lamb from the smoker and let it rest for 10–15 minutes. While the lamb is resting, preheat the oven broiler on high.
Transfer the lamb to the oven and broil for a few minutes, turning as needed, until a browned crust forms on the outside.
Remove the lamb from the oven and let it rest for 10–15 minutes.