In a medium sauce pan, add lime juice, lime zest, water and caster sugar.

Simmer until syrup consistency and the sugar is fully dissolved.

Set aside to cool.

Once the syrup has cooled, stir in milk.

Chill the base mixture until you are ready to make the ice cream.

Make the ice cream to the manufacturer's instructions of your ice cream maker.

If you don't want to use an ice cream maker, pour the base into a freezer safe container.  Put in freezer.  Stir every few hours until "soft set" then let freeze until hard.