Put the sugar, water, and corn syrup in a saucepan and heat until the sugar is dissolved, stirring occasionally. Carefully, transfer the mixture to a container and cool in the refrigerator without a lid, or place the container in an ice bath.
Without peeling, cut the apple away from the core. Cut the apples into a large dice and toss with 1 tablespoon fresh lemon juice.
Add the apples and cooled syrup to a blender and puree until smooth. Strain the mixture and add the remaining 1 tablespoon lemon juice right away. Refrigerate, about 1 hour. Remove from the refrigerator and pour into the bowl of an ice cream machine. Freeze according to the manufacturer's instructions.
If you don't have an ice cream machine, try freezing 1/2 the mixture in ice trays and processing it in a blender with the remaining liquid. Then place in the freezer to firm up.