I know what you're thinking. Avocados in a sorbet? Oh, just you wait. The coconut and lime add a tropical panache, but the avocado gives it a very distinctive, smooth finish. I can't think of a more gratifying way to get a healthy scoop of monounsaturated fats.
In a medium saucepan, combine the water and sugar and cook over high heat. Bring to a boil, reduce the heat, and then simmer until the sugar has dissolved, stirring frequently. Remove from the heat and set aside. Pour the contents of the saucepan into a large bowl and stir in the lime zest; chill the mixture in the refrigerator for at least 1 hour.
Meanwhile, place the lime juice, avocados, cream of coconut, and salt in a food processor and blend until smooth. Add the chilled mixture and pulse to combine. Pour the contents of the food processor into an ice cream maker or a Vitamix, and follow the manufacturer's directions. Serve immediately or store in an airtight container in the freezer.