Heat 1 cup water with the sugar until dissolved. Place in the fridge till cold. Combine the sugar syrup with the lemon juice and cold water. Blend together. Pour into a freezer-safe container. Freeze, stirring and scraping the mixture with a rubber spatula at first, and then with the tines of a fork ever 30-40 minutes until a grainy consistency and completely frozen. This will take about 3 to 4 hours. Pour a glass of ice tea, spoon in the granita.
Marcella Hazan provides a little more complicated process. Pour 1/2 cup lemon juice, 1 1/2 cups water, and 1/4 cup sugar. Pour in freezer trays. Let sit for 15 minutes in freezer. Then stir to break up the ice crystals along the sides. Repeat again in another 15 minutes. Then repeat in 10 minutes, then 8 minutes for the next few hours