Combine apple juice and cinnamon sticks in a large saucepan. Simmer 5 minutes, and set aside. Next, combine the sugar and water in a medium saucepan. Boil to 260*F. Add apple juice and corn syrup to sugar syrup. Boil 5 minutes. Remove the cinnamon sticks. Stir in the lemon juice. Ladle the hot syrup into hot jars, leaving 1/4" headspace. Adust caps. Process in a boiling water canner 10 minutes.