In a medium saucepan, combine equal parts granulated sugar and water over medium heat. Stir continuously until the sugar dissolves, about 3-5 minutes. Remove from heat and let cool.

While the sugar syrup cools, peel and quarter the ripe kiwis. Place in a blender and puree until smooth, about 30 seconds.

Strain the kiwi puree through a fine mesh sieve into a large mixing bowl, pressing with a spatula to extract as much liquid as possible. This should take about 2-3 minutes.

Mix the cooled sugar syrup with the strained kiwi puree. Add lemon juice and whisk until combined. Taste and adjust sweetness if needed. Cover and refrigerate for at least 2 hours.

Pour the chilling kiwi mixture into an ice cream maker and churn according to instructions for 20-25 minutes until fluffy. Alternatively, pour into a shallow container and freeze, stirring every 30 minutes for 2-3 hours.

Scoop the kiwi sorbet into chilled bowls or cones and garnish with kiwi slices or lime zest. Enjoy immediately or store in the freezer for up to a week.