In a small saucepan, combine sugar and water. Heat over medium, stirring until the sugar dissolves. Let cool completely.
Add chopped kiwi, lemon juice, and the cooled syrup to a blender. Blend until smooth.
Strain the mixture through a fine mesh sieve to remove seeds, if desired.
Pour the mixture into a shallow dish or loaf pan and freeze for 3–4 hours, stirring every 30 minutes to break up ice crystals.
Once fully frozen, scoop and serve immediately for the best texture.