Put the sugar and water into a saucepan and bring to the boil, stirring until the sugar has dissolved. Pour the syrup into a bowl, leave to cool and then chill.
Puree the fruits in a food processor or blender, then press through a sieve into a large bowl. Stir in the chilled syrup and lemon juice.
If you have an ice cream maker - churn until thick enough to scoop. If you are making by hand-pour the mixture into a plastic container and freeze for 4 hours until mushy.
Transfer to a food processor and process until smooth, then return to the container.