Stir the ginger, water and lemon juice together. Stir in the sugar and pour the mixture into a 9- by 9-inch baking pan. Cover and put into the freezer.
After 1 hour, using a fork, scrape the frozen top layer. Scrape and break frozen blocks into pieces. Continue to scrape every 15 to 20 minutes until the granita has a fluffy, snow consistency, about 2 hours. Eat immediately or keep for 3 days in the freezer, scraping every so often