Bring 3/4 cup water and sugar to boil in heavy medium saucepan, stirring until sugar dissolves. Mix in sweetened condensed milk, then lime 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 manufacturers instructions. Transfer sorbet to medium container, cover, and freeze until firm, at least 4 hours and up to 2 days.