In the bottom of each glass, place 1 teaspoon of lemon juice and 1 teaspoon of butterscotch topping. Stir together until blended. Add apple juice until the glasses are 3/4 full. Stir well to combine the apple juice with the butterscotch mixture. Fill the glasses with ice cubes. Garnish with apple rings and cinnamon sticks. Rub a cut lemon over both sides of the apple rings to prevent the apple flesh from turning brown.