In a medium saucepan over medium heat, combine 3/4 cup granulated sugar and 1 cup water. Stir until the sugar dissolves, which should take about 5 minutes. Remove from heat and let cool.

Peel and quarter the 6 ripe kiwis and place them into a blender. Blend on high until smooth, typically about 1-2 minutes.

Optionally strain the blended kiwi puree through a fine mesh sieve into a mixing bowl to remove seeds and pulp for a smoother texture.

Combine the strained kiwi puree, cooled sugar syrup, and juice of 1 lemon in a large mixing bowl. Cover and refrigerate for about 2 hours.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions for about 20-30 minutes.

For a softer sorbet, serve immediately. For a firmer texture, transfer to an airtight container and freeze until solid, about another hour.