Place sugar in a blender; process until very finely ground. Add basil; process until finely minced. Pour into an 8-inch square glass or ceramic baking dish.
Combine peach slices, 2/3 cup water, and lemon juice in blender; process until smooth. Pour juice mixture over sugar mixture, and stir until sugar dissolves. Cover and freeze until partially frozen (about 1 hour). Scrape with a fork, crushing any lumps. Freeze, scraping with a fork every hour, 4 hours or until completely frozen and fluffy.