In a 4- to 6-quart Dutch oven, combine cider, lemon juice, and sugar. Bring to boiling, stirring to dissolve sugar. For spice bag, place cinnamon and cloves in center of a double-thick, 6-inch square of 100-percent-cotton cheesecloth. Tie closed with a clean string. Add spice bag and 3 sliced oranges to the cider mixture.
Reduce heat. Simmer gently, uncovered, for 30 minutes. Remove spice bag and oranges and discard. Serve cider in mugs. Float orange slices in each mug, if you like. Makes 16 (about 8-ounce) servings.