Using a vegetable peeler, remove the zest from each lemon. With a vegetable peeler remove zest in long pieces. Squeeze juice from the lemons until you have 1/2 cup.
In a small heavy saucepan heat 1 cup water and 1/3 cup sugar, stirring until all the sugar is dissolved. Stir in zest and transfer syrup to a bowl, set aside until cool. Discard zest and stir in lemon juice. Taste to see if it’s sweet enough. If you want more sweetness, heat 1/2 cup water with 1/2 cup sugar and stir until sugar is completely dissolved. Once the sugar mixture is cooled, add a small amount at a time to the lemon juice until it reaches the level of sweetness you like.
Pour the lemon mixture in a shallow roasting dish. I find that a 13x9 inch glass dish works the best. You don’t want the mixture to come up more than an inch on the sides, or it will take forever to freeze.
Put it the freezer for about 3 hours, depending on the strength of your freezer. Every hour, take it out and scrape it with a fork to loosen up the ice crystals.
When the granita is completely frozen, before serving scrape again.