Bring the water to a boil and dissolve the sugar in this. Let cool. Scrub the limes clean.
Zest two limes (see how to zest a lime HERE) and then juice them.
Mix 3 tbsp. lime zest, 4 tbsp. lime juice, coconut milk, and triple sec into the sugar water.
Let this churn in the ice cream maker for 30 minutes until it’s frozen, or place this in a deep dish in the freezer and let freeze for 6 hours. In the latter case, stir the mixture thoroughly every hour using a fork.
Cut the last lime into thin slices and then halve these. Garnish every scoop of ice cream with half a slice of lime.