Preheat an oven to 300°F. Rub the lamb with oil and season generously with the salt and pepper.
Heat a large roasting pan over medium-high heat. Add the lamb and cook, turning occasionally, until browned on all sides, 10 to 12 minutes. While the lamb is cooking, add the halved lemons as well, and cook, cut side down.
Once the lamb is browned on all sides, add the wine, leeks, garlic, and herbs. Using tongs, remove the lemons to cool slightly, then squeeze the juice over the lamb. Add the spent halves to the pan.
Tent the lamb with foil. Transfer to the oven and roast, turning the lamb occasionally and making sure the bottom of the pan is moist, not dry, for 3 hours. Uncover, turn the lamb, and add 4 cups of the chicken stock, stirring to combine with the cooking liquid. Tent the lamb, once again, and continue to cook, turning occasionally and adding 4 more cups of stock as needed and basting occasionally, until the lamb is very tender, 4 more hours. (The cooking liquid will darken over the course of cooking, but the base of the roasting pan should never become dry or burnt. If so, add more of the chicken stock, or even water. Don’t fret—it doesn’t require constant babysitting; just take a peek every hour or so.)
After 7 hours of cooking, transfer the lamb to a warmed platter and tent once again with the foil to keep warm. By now, the lamb is practically falling off the bone. Put the roasting pan with cooking liquid and vegetables over low heat. Add the remaining 2 cups of chicken stock and stir to combine. Bring to a boil, then reduce the heat to maintain a simmer. Let the liquid simmer while the lamb rests, about 10 minutes. Strain the cooking liquid, pressing on the solids, through a fine-mesh sieve into a medium saucepan.
Discard the solids; taste and adjust the jus for seasoning with salt and pepper.
Remove the foil from the lamb and baste with some of the jus. Serve the lamb with the jus on the side.