Wrap cloves, allspice, cinnamon sticks, and lemon zest in a small piece of cheesecloth and tie packet with kitchen twine to close it. In a medium saucepan (not aluminum), combine spice packet and cider. Cover and bring to a simmer over high heat. Remove from heat and let stand, covered, about 1 hour.
To serve, heat infused cider, covered, over medium heat until hot and steaming. Lift out and discard spice packet. Stir in rum. Ladle into cups or heatproof glasses and garnish with lemon slices if you like.
Note: Nutritional analysis is per 3/4-cup serving.