Stir together first 6 ingredients in a large bowl, stirring until well blended.
Pour lime mixture into freezer container of a 4-quart ice-cream maker; freeze according to manufacturer's instructions. Garnish each serving, if desired.
Refreshing Lemon Sherbet: Substitute a large lemon for the lime and fresh lemon juice for lime juice. Proceed as directed. Garnish with fresh mint sprigs, thinly sliced lemon wedges, and lemon rind strips.