Combine the sugar and 1 cup water in a saucepan. Bring to a boil and stir until sugar is dissolved. Remove from heat and place in the refrigerator until cold, about 1 hour.

Using the finest grater you have, lightly scrape the skin of 1 lemon, removing only the top surface of the peel. Squeeze out the juice and remove the seeds from both lemons.

Open the Champagne or sparkling wine, and pour it into a 9 by 12 by 2-inch pan. Mix in the simple syrup, lemon juice, and grated zest. Place mixture into the freezer. Check after 30 minutes. Using a wooden spoon, break up any ice formed on the sides and stir into the rest of the liquid. Continue to freeze and repeat this procedure every hour for at least 3 hours. Before serving, fluff the granita by "chopping" up any clumps with the spoon or gently whisking the frozen mixture. Spoon into small glasses or cups and serve.