Make simple syrup: Add sugar to water in small saucepan. Stir over medium heat until sugar is fully dissolved. Raise heat and bring syrup to a boil; boil one minute, then remove from heat and allow to cool completely.
Puree thawed mango and lime juice in a food processor.
Stir simple syrup into mango puree. Refrigerate a few hours to be certain puree is cool.
Follow the manufacturer's instructions for your ice cream maker at this point. If you don't have one, pour into a pan and put in freezer; pull out every hour and stir (for 3-4 hours).