In a medium, nonreactive saucepan, blend 1/2 cup of the water with the sugar. Add lemon zest. Heat, stirring frequently, until the sugar has completely dissolved. Remove from the heat, add vanilla extract and remaining water, then chill in the refrigerator.
When the mixture is cold, add the lemon juice and pour into a nonreactive container and place in the freezer.. When it freezes around the edges, take a fork and stir the mixture, breaking up the frozen pieces into smaller pieces and push them toward the center of the container. Put the mixture back in the freezer. Check again every 30 minutes, stir, and break any chunks into smaller pieces with a fork until you have small crystals of granita. If it freezes too hard at any point, let the mixture sit out until it is soft enough to stir, and break it up again.
Serve in glasses or bowls, over fruit or gelato, add sweetened whipped cream, or add some alcohol and use the granita as flavored ice.