Remove fell (paper-thin, pinkish red layer) from outer surface of meat, trim fat from meat.
Combine parsley, basil, salt, and pepper; rub over lamb.
Insert a meat thermometer near the center of the roast, not touching the bone.
Place lamb in center of the cooking grill.
Grill 1 1/4 hours or till meat thermometer registers 140°F (60°C).
Remove lamb from grill.
Transfer to an 11 x7-inch roasting pan.
Combine water, tomato sauce, lemon juice, and garlic; pour over lamb.
Toss together artichoke hearts and olives; arrange around lamb.
Return lamb in roasting pan to cooking grill.
Grill about 30 minutes more or till meat thermometer registers 160°F (71 °C), basting occasionally with sauce, if desired.
Let roast stand 15 minutes before carving.
Transfer roast to a serving platter.
Using a slotted spoon, arrange artichoke mixture on serving platter with lamb.
Drizzle with any remaining sauce.
Pass feta cheese.