Put the olive oil in a braising pan large enough to hold the lamb snugly with minimal overlap. Place the pan over high heat. When the oil is hot, put in half the lamb and brown lightly on both sides. Transfer to a platter and repeat with the remaining lamb. When all the meat is done, season it with salt and pepper.
While the lamb is browning, peel and finely chop the garlic and chop enough of the thyme leaves to measure 1teaspoon. After the lamb is out of the pan, lower the heat to medium-high. Put the garlic and thyme in the pan and stir well. Add the wine and let it bubble away for 30 seconds to let the alcohol evaporate. Return the meat to the pan. Adjust the heat so that the liquid in the pan simmers and cover with the lid askew. Cook, turning the meat every 15 to 20 minutes, until the lamb is almost fully tender, about 1 hour. If all the liquid evaporates before the lamb is done, add a little water.
While the meat is cooking, trim the artichokes as described and cut them into wedges about ¼ inch thick. Use half of one of the lemons to rub the cut parts of the artichokes as you are trimming them and squeeze the other half into a large bowl of water. Put the artichoke wedges in the bowl of lemon water.
After the lamb has cooked for about 1 hour, drain the artichokes and add them to the pan. Season with salt, cover the pan, and cook until the artichokes are quite tender, at least 30 minutes more. If all the liquid dries up before they are done, add some water. If there is still a lot of liquid in the pan when the artichokes are done, remove the lid, raise the heat, and let it evaporate until the sauce is thick enough to coat a spoon. Squeeze the remaining lemon and add about 2tablespoons juice to the pan.
This dish can be prepared 1 to 2 days ahead. When ready to serve, gently reheat it with the lid on and add the lemon juice just before serving.