Step 1In a blender, puree the currants with the raspberries. Press them through a stainless steel or nylon sieve (wire discolors the fruit) into a medium bowl, and add the lemon juice.
Step 2In a medium saucepan, bring one-half cup of water and the sugar to a boil. Boil until the mixture is a light syrup consistency, 4 minutes (for a more dense sorbet, boil until the syrup is thick, 7 minutes). Cool for a few minutes.
Step 3Stir the currant and raspberry mixture into the sugar syrup. Place the granita in a large glass baking dish, cover loosely with foil and allow to freeze, 2 to 2 1/2 hours.
Step 4Ten minutes before serving, transfer the granita to the refrigerator to soften. Serve.