Combine first 3 ingredients in a large nonaluminum saucepan; bring to a boil. Add lime rind, and cook over low heat 10 minutes, stirring occasionally. Strain mixture through a sieve into a bowl, reserving the sugar mixture. Discard solids. Cool sugar mixture completely. Stir in lime juice.
Pour the juice mixture into the freezer can of an ice-cream freezer, and freeze according to the manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze for 2 hours or until firm.