Special equipment: 5 to 6 (1/3-cup capacity) popsicle molds
In a medium saucepan, bring the apple juice, sugar, lemon juice, salt, ginger, cinnamon stick and allspice berries to a boil over medium heat. Remove the pan from the heat and let the mixture stand for 15 minutes. Strain the mixture into a large measuring cup.
Pour the mixture into ice pop molds. Insert the stick/cover tops and freeze until solid, about 6 hours.
Run cold water over the sides of the molds to loosen the ice pops and serve immediately