1) Take a Dutch oven and mix together apple cider, juice cocktail, brown sugar, cinnamon, cloves and lemon in it. Bring the mixture to a boil.
2) Reduce heat and simmer for about 15-20 minutes.
3) Strain cider, discarding lemon and spices.
4) Serve the Spiced Cranberry Cider hot with additional cinnamon sticks, if desired.