Purée the raspberries in a blender or food processor, and strain through a sieve.
Put the sugar and 300ml/10fl oz water in a heavy saucepan, and boil for 5 minutes. Remove from the heat and allow to cool. Add the lemon juice and 100ml/3 1⁄2fl oz water and the raspberries.
Freeze the mixture overnight in a shallow freezer container, occasionally breaking up any large crystals with a fork if necessary.