Heat 1 cup water in a saucepan and stir in the sugar until dissolved. Let cool, and then add in the lemon juice and rinds. Taste and make adjustments as necessary with more sugar and lemon juice. Freeze the lemon mixture in a metal bowl, stirring every 20 minutes, until the liquid has become granular but is still slightly slushy, 3 to 4 hours. Serve the granita immediately.