Heat the granulated sugar and water in a small saucepan, stirring frequently until the sugar has completely dissolved. This is a sugar syrup and it will help your sherbet have a smooth texture.
Remove the pan from the heat and stir in the lime juice and zest. Refrigerate the mixture until it is completely chilled. Stir the milk and green food coloring into the lime juice.
Churn the mixture in the ice cream maker
Store in the freezer until eatten