Place a baking dish in the freezer. Zest and juice the limes. Reserve zest. Cut melon into chunks, slicing the skins off and discarding them as you go. Add the sugar with equal parts water to a small pot set over medium heat, and reduce to a simple syrup. Let cool.
Add the melon, lime juice, half of the lime zest, and cooled simple syrup to a blender. Process until smooth. Pour into the chilled baking dish and freeze for approx. 2.5 hours, scraping the mixture with a fork every half hour until the mixture is fluffy and soft.