Use an ice cream maker.
In a small saucepan, over medium-high heat, combine the sugar and 1 cup water. Bring to a boil and simmer, stirring, until the sugar dissolves, 3 minutes. Transfer to a bowl and chill over an ice bath until cool. Stir in the lemon zest and juice.
Follow the manufacturer's instructions for freezing. Serve immediately or freeze in an airtight container.