Heat the oven to 450 degrees. If the leg of lamb is tied, untie it, unroll it and lay it skin-side down on a cutting board. (If necessary, use a sharp knife to make a few cuts to flatten the meat evenly.) Combine the garlic, rosemary, lemon zest, 1/2 teaspoon salt and 1/4 teaspoon pepper in a small bowl. Add enough olive oil to create a paste, and evenly spread this over the cut surface of the lamb. Roll the lamb up tightly and evenly and secure it with kitchen string. Rub the surface of the lamb with the softened butter, and season generously with salt and pepper.
Set the lamb in a large roasting pan. Evenly scatter the sliced onion and potatoes all around the lamb. Drizzle them with about 1/4 cup olive oil and season with salt a pepper. Place the roasting pan in the oven and cook for 20 minutes. Stir the potatoes once, lower the heat to 325 degrees and cook for about another hour (until a thermometer inserted into the thickest part of the lamb registers 135 degrees), stirring the potatoes once or twice during this time.
In the meantime, heat the cider vinegar and sugar in a small saucepan, stirring until the sugar dissolves. Stir in the mint and set aside to cool. When the lamb is finished, remove it from the roasting pan to a cutting board and allow it to rest for 15 to 20 minutes. Keep the potatoes warm. Slice the lamb against the grain and serve it with the potatoes and mint sauce on the side.