With a vegetable peeler remove zest in long pieces from 2 lemons. Squeeze 1/2 cup juice from lemons. In a small heavy saucepan heat and sugar, stirring until sugar is dissolved. Stir in zest and transfer syrup to a bowl to cool. Chill syrup, covered, until cold. Discard zest and stir in lemon juice.
For eastern-Sicilian granita: Freeze lemon mixture in an ice-cream maker until spoonable but not crumbly and serve immediately.