Combine lemon juice, lemon rind, and sugar in medium bowl; refrigerate for 24 hours.
Pour mixture into freezer can of 5-quart hand-turned or electric freezer. Add half-and-half and whipping cream. If necessary, add milk until mixture reaches fill line in freezer can. Freeze according to manufacturer?s instructions. Let ripen at least 30 minutes before serving. Makes 5 quarts.