1. Combine water and sugar in a small sauce pan over low heat and stir until sugar is dissolved, making a simple syrup. Remove from heat.
2. Using a vegetable peeper, peel the zest off of one lemon leaving as much of the pith on the lemon as possible. Stir the lemon zest into the sauce pan with the simple syrup. Let sit until it cools to room temperature. Once cool strain the mixture into a bowl, and discard the lemon zest.
3. Juice the lemons to make 1/2 cup of lemon juice. Stir the lemon juice into the bowl with the syrup.
4. Transfer the mixture to a flat metal pan and pace in the freezer. Every 30 minutes take the mixture out and stir it up with a fork, breaking up any ice crystals that form. Do this for 3-4 hours. As the mixture gets more frozen you will be scraping the ice with the fork to mix it up.
5. If you want a granita that is more slushy to be eaten immediately, stop after 3 hours. If you want one that is more granular that will store for a couple of days in the freezer go to 4 hours scraping the frozen mixture with the fork to create ice crystals.

Alternate Method

1. Follow steps 1 through 3 above, then process mixture in an ice cream maker until the granita is slushy with little chunks of soft ice, 20-30 minutes.