Place A Non-Reactive roasting pan or gratin dish in the freezer. Bring sugar and water to a boil in a saucepan, stirring occasionally to dissolve sugar. Cool the syrup. Stir in the lemon juice and pour through a fine strainer to eliminate any seeds or pulp. Pour into the prepared pan and return to the freezer. When the mixture starts to freeze, stir every 10 minutes or so, scraping the frozen mixture from the bottom and sides of the pan and mixing it with the as-yet-unfrozen mixture. When there is no longer any unfrozen liquid in the pan, pack the granita into a chilled container and press plastic wrap against the surface. Serve within a few hours for best texture. If the granita freezes to a solid block, pop it out of the container and cut into thick slices with a stainless steel knife.
Chop the slices finely, replace in the container and freeze until serving time. Serve the granita in chilled stem glasses. Substitute lime or grapefruit juice for distinctly different flavors.
