Make Sugar Syrup: Combine the sugar and water in a saucepan over medium heat. Stir continuously until the sugar is fully dissolved. Allow the syrup to cool to room temperature.

Blend the Kiwis: Place the kiwi quarters in a blender and blend until you get a smooth puree.

Strain for Smoothness: For a finer texture, pour the kiwi puree through a fine mesh sieve to remove the seeds.

Mix and Chill: In a bowl, combine the strained kiwi puree with the cooled sugar syrup and lemon juice. Place the mixture in the refrigerator and chill for about 2 hours.

Freeze the Sorbet: Pour the chilled mixture into an ice cream maker and follow the manufacturer's instructions. If you don’t have an ice cream maker, transfer the mixture to a shallow dish and freeze it, stirring every 30 minutes, until it reaches a sorbet-like consistency.

Serve: For a soft sorbet, serve immediately. For a firmer texture, store in an airtight container and freeze until solid.