Discard the meat's tough membrane and excess fat and place the lamb in a large baking dish. Turn on a blender or food processor and drop the garlic onto the spinning blades. Turn off the machine, add the remaining ingredients, and blend to a paste. Spread the paste over the lamb. Cover and let marinate in the refrigerator 2 to 8 hours.
Preheat the grill with all the burners on high. After 15 minutes, turn off the center burners and reduce the outer burners to medium. (If using charcoal, light 50 briquettes and let them burn until they are covered with gray ash. Push them into 2 banks on either side of the grate. Place a drip pan between the coals. Replace the grate.) Grill the lamb, with the grill covered, for 1 1/4 to 1 3/4 hours. (If using charcoal, add 10 briquettes after 1 hour to maintain heat.) The lamb is done when it registers 140° F on an instant-read thermometer. Let rest at room temperature for 15 minutes before carving.
Rainy-Day Method: Prepare the lamb as above, but roast on a rack in a roasting pan in a 325° F oven for 1 1/2 to 2 hours or until an instant-read thermometer inserted into the meat registers 140° F. Let rest 15 minutes before carving.