Combine water, cinnamon sticks, cloves, and allspice in a large pot; bring to a boil, reduce heat to medium-low, and simmer until flavors combine, about 10 minutes. Strain and discard spices. Return spiced water to the pot.
Stir apple juice, orange slices, and lemon slices into spiced water. Cook over medium-high heat until heated through, 10 to 15 minutes.