Thinly pare the rind from the lime and put it in a small saucepan with the caster sugar and water. Squeeze the lime juice into the pan. Bring to the boil and simmer for 6–8 minutes until the volume is reduced roughly by half and is lovely and syrupy. Remove from the heat, and allow to cool to room temperature before removing the zest.
For the granita put the cooled syrup, watermelon chunks and strawberries in the bowl of a food processor and pulse until smooth. Pour into a shallow baking dish (use either ceramic or metal but the metallic dish will freeze the fastest) and spread the bright red pulp evenly. Transfer to a freezer and freeze the mixture until edges begin to set, 30–35 minutes. Using a fork, scrape to break up frozen portions. Freeze, scraping and breaking up every 20–30 minutes, until mixture resembles fluffy shaved ice, total time will be 2–4 hours.
Serve the frozen ice in bowls, garnished with fresh strawberries.