In a medium saucepan, combine 1/2 cup of water with the sugar.
Add the zest of 2 lemons directly into the mixture.
Heat, stirring frequently, until the sugar dissolves into the simple syrup.
Remove from the heat and add the remaining 2 cups of water.
Chill thoroughly in the refrigerator.
Then, add in the lemon juice into the cold simple syrup.
Freeze mixture in ice cream maker according to the machine's instructions (mine takes about 25-30 minutes).
Transfer in an airtight container and freeze until ready to serve.