Start by peeling the brown furry-ness off, and dicing into pieces.
Then put all the kiwi into a food processor or blender and puree to make about 2 cups
In a small sauce pan bring the 1 cup water and 1/2 cup sugar to a boil to make a simple syrup. Remove from heat and let it cool. ( I poured the syrup into a glass measuring cup and put that into an ice bath to hurry up the cool down time).
Pour kiwi puree, syrup, and 2 tbsp lemon juice into the ice cream maker and follow the manufacturer's instructions.