Whisk the mango nectar, sugar, sweetened lime juice together, and vodka in a large measuring cup to dissolve the sugar. Chill in the refrigerator for 2 to 3 hours, until cold.
Pour the mango mixture into an ice cream machine and churn until frozen and slushy, following manufacturer's directions. Freeze until solid, another 2 to 3 hours.
Cook's Note: The vodka helps make the sorbet more scoopable without adding flavor.