In a saucepan over medium heat, combine the sugar and water. Stir until the sugar fully dissolves, then remove from heat and let cool to room temperature.
Add the peeled, quartered kiwis to a blender and puree until smooth.
For a smoother sorbet, strain the kiwi puree through a fine mesh sieve to remove the seeds.
Combine the strained kiwi puree with the cooled sugar syrup and lemon juice. Mix well.
Refrigerate the mixture for about 2 hours until thoroughly chilled.
Pour into an ice cream maker and churn according to manufacturer’s instructions.
If not using an ice cream maker, pour the chilled mixture into a shallow container, freeze, and stir every 30 minutes until it reaches sorbet consistency.
Serve immediately for a soft texture or freeze in an airtight container until firm.