In a small sauce pan whisk together water and sugar, and bring to a boil. Immediately remove from heat. Stir in lemon zest, and allow to cool completely. Add lemon juice, and chill for at least two hours.
Wash apricots and chill them along with the lemonade. Do NOT pit them, yet, as they start turning brown pretty quickly. Right before you’re ready to freeze the sorbet, pit the apricots.
In a blender, combine apricots and lemonade and blend until smooth. Immediately pour into ice cream maker, and freeze according to directions. When finished, transfer to air tight freezer container, and freeze several hours.
Notes
Makes 1½ quarts. If you have a 4-quart ice cream freezer, and want to make a large batch, times the recipe by 3. If you have a 6-quart, times it by 4.