Add the quince, cover with the water, and bring to a boil. Reduce the beat to medium-low and cook for 1 hour, uncovered. Add the sugar and stir. Cover and cook until the lamb is very tender and the quince soft, about another hour. Remove to a serving platter with a slotted spoon and serve.
Quince are like very hard apples.
Although there is a sweet variety in North Africa, the quince available in American markets are inedible in the raw state. Use a sharp knife and don't cut them up until you need them because they discolor.