1. To make sugar syrup, add sugar and water to a small saucepan and stir over a low heat until the sugar has dissolved. Remove from the heat and cool.
  2. Using a blender, blend the sugar syrup, berries and lime juice. Strain through a sieve and then churn using an ice cream maker until the sorbet has reached a thick and icy consistency.
  3. Freeze for up to 2 weeks.