Season the lamb with 2 teaspoons kosher salt and generously pepper to taste. Roast, fat side up, on a rack in a roasting pan until a meat thermometer inserted into the thickest part of the meat registers 130°F, or medium-rare, about 60 to 80 minutes.
Remove the lamb from the oven and let it rest for 30 minutes. Slice, transfer to a platter, garnish with olives, purslane, and grilled lemons, and serve.