Place an 8 inch square baking tin in the freezer.
Place the caster sugar and water in a saucepan for the sugar syrup and bring to a simmer over a medium heat. Stir to help dissolve the sugar as the mixture as it comes to a simmer. Reduce the heat and continue to cook for 2-3 minutes until the syrup has thickened a little. Remove from the heat and set to one side, allowing it to cool to room temperature.
Place the strawberries and lime juice in a food processor and blitz until you have a smooth purée. Add the cooled sugar syrup and pulse a couple of times to just incorporate. Pour the mixture into the frozen baking tin and freeze for 1 hour. Remove after one hour and use a fork to break up the frozen mixture, whisking to break up as evenly as possible. Return to the freezer for 90 minutes.
Remove and break up with a fork once again in the same manner as before. Before you serve the granita, run a lime wedge around the rim of 4 martini glasses. Place the 2 tbsp of caster sugar on a small plate, covering the surface evenly, then invert the glasses and dunk in the sugar in order to coat the rims. Place in the freezer for a few minutes.
Spoon the granita into the prepared martini glasses and place a lime slice in the rim to garnish.