1) Combine the sugar and water in a small saucepan and place over low heat. Stir until the sugar dissolves completely and the syrup is clear. Remove from the heat and allow to cool to room temperature.
2) Peel the mangoes and cut as much of the fruit as you can away from the large pits. If the mangoes are very ripe and juicy, and you feel adventurous, squeeze the pulp and juice off the pits with your hands. It's messy work, so do it over a large bowl.
3) Combine the cooled syrup, mango pulp and lime juice in a blender or food processor. Blend until completely smooth, about 30 seconds. Cover and refrigerate until cold, or overnight.
4) Stir the chilled mixture, then freeze in your ice cream machine according to the manufacturer's instructions. When finished the sorbet will be soft, but ready to eat. For firmer sorbet, transfer to a freezer-safe container and freeze at least 2 hours.
Makes about 3 cups