In a medium bowl stir together wine and sugar until sugar is completely dissolved.
In a food processor or blender combine apples, lemon juice, and 1/2 cup of the apple juice. Cover and process or blend until smooth. Press mixture through a fine-mesh strainer, reserving apple liquid. Discard pulp. Add enough of the remaining apple juice to strained apple mixture to equal 2-1/2 cups. Stir in wine mixture.
Transfer mixture to a 3-quart rectangular baking dish. Freeze about 1-1/2 hours or until slushy. Stir with a fork; freeze for 1-1/2 to 2 hours more or until set. Using a fork, scrape granita into flakes.
Spoon granita into wineglasses and top with strawberries and/or apple slices.