First, make the simple syrup: add 2 cups of sugar to 2 cups of water over medium heat.
Cook gently until the sugar is dissolved and the liquid is perfectly clear, so that you can see the bottom of the pan. DO NOT boil it, this can cause sugar crystallization. Refrigerate overnight.
Mangos can be a little tricky to prep. Stand it in end, and slice down one side, cutting off the whole lobe. Be careful not to cut too close to the pit, the flesh there can be very fibrous and chewy.
Rotate the mango 180 degrees and slice off the opposite lobe.
Holding one love in the palm of your hand, cut a grid into the mango flesh, making 1/4" squares. Careful not to use too much pressure, you don't want to cut through the skin.
Add the mango to a blender. Juice all three limes into the blender.
Add 1 cup simple syrup.
Blend until very smooth. It's important to have the right sugar concentration. Too much sugar and your sorbet won't set up, too little sugar and it will freeze rock hard. Use the egg trick to check:
The egg trick: float a raw, washed egg in the purée. The egg should sink so a circle the size of a nickel is showing. If more egg is showing, add more purée. If less egg is showing, add more syrup.
Once the sugar balance is right, add the purée to an ice cream maker. Freeze following manufacturers directions.
The sorbet should thicken up quite a bit. Once it's done, put it in a freezer-safe container and freeze overnight to set completely.
Garnish with lime zest.