Bring 3/4 cup water and sugar to boil in medium heavy saucepan, stirring until sugar dissolves. Mix in sweetened condensed milk, then lie juice. Transfer mixture to medium bowl; place over large bowl filled with ice and water and cool, stirring often, about 30 minutes.
Process lime mixture in ice cream maker according to manufacturer's instructions. Transfer sorbet to medium container, and freeze until firm, at least 4 hours and up to 20 days.