Prepare Simple Syrup:

In a small saucepan, combine sugar and water. Bring to a boil, then reduce heat and simmer until the sugar has dissolved completely. Remove from heat and let cool.

Blend the Kiwis:

In a blender or food processor, puree the sliced kiwis with the lime juice until smooth.

Combine and Chill:

Mix the cooled simple syrup with the kiwi puree. Pour the mixture into a bowl and refrigerate until completely chilled, about 1-2 hours.

Churn or Freeze:

If using an ice cream maker, churn the mixture according to the manufacturer's instructions. Otherwise, pour the mixture into a freezer-safe container and freeze, stirring every 30 minutes to break up ice crystals, until firm.