Poach the pears: Combine the sugar, water, spices, and lemon slices in a saucepan. Boil 5 minutes. Add the pear halves, reduce the heat to low, and simmer until the pears are translucent and cooked through but not mushy, about 25 minutes. Remove the pears from the syrup with a slotted spoon; let cool. Reserve about
Meanwhile, prepare the sauce: Heat the butter in a large sauté pan or skillet over medium heat. Add the onion, carrot, and celery;
Cut the duck into quarters (or eighths if you prefer) and warm in a 400°F oven about 5 minutes. Heat the sauce to simmering over medium heat, add the pear slices, and simmer until heated through. Arrange 2 duck quarters on each of 4 serving plates and spoon the sauce and pears over top. Serve with roasted potatoes and sautéed spinach with pine nuts and raisins.