Tip the sugar and water into a small saucepan, heat gently, stirring occasionally, until the sugar has dissolved then bring to the boil and cook for 1 minute.
Purée the strawberries in a blender or food processor until smooth then press through a sieve to remove the seeds. Stir into the sugar syrup with the lemon juice and vodka. Pour into a shallow container so that the syrup is no more than 2.5 cm (1 inch) deep, cover and allow to cool.
Transfer the dish to the freezer and freeze for 2 hours until just beginning to set around the edges of the dish. Break up the icy edges with a fork and return to the freezer. Beat with a fork every 30 minutes or so over a 2 hour period until the mixture has formed tiny ice crystals and looks like crushed ice. Freeze until required.
When ready to serve, remove the frozen granita from the freezer and leave at room temperature for 15–30 minutes until soft enough to mix. Spoon into tiny glasses set on small plates and decorate the plates with tiny halved strawberries, if liked. If feeling generous, drizzle with a little extra vodka.