Using a vegetable peeler, zest long strips from 2 of the lemons and set aside. Juice the lemons through a fine mesh strainer.
Combine the water and sugar in a saucepan and simmer on medium heat until the sugar dissolves.
Take the pot off the heat and add the zest and mint. Allow the flavors to steep for 30 minutes while the mixture cools.
Strain the zest and mint from the sugar syrup and stir in the lemon juice.
Pour the mixture into a brownie pan or flat-bottomed glass dish. Place in the freezer for 30 minutes.
Stir the mixture very thoroughly with a fork and allow it to freeze for another 30 minutes.
Repeat this process every 30 minutes for 3-4 hours. Make sure to mix the granita well every time, scraping down the sides. The idea is to prevent ice crystals from forming so you wind up with a consistency similar to sorbet. If the mixture isn't stirred thoroughly you might wind up with small blocks of ice, which aren't nearly as fun to eat. 3 hours will give you a good granita, 4 hours will guarantee the consistency if you're not planning to serve it immediately. I recommend serving within 24 hours.