Place a small baking dish in the freezer to chill.
Scoop the fruit from the watermelon, leaving behind the peel and rind. Place in a blender and pulse until thin and even.
Pass the watermelon juice through a fine-mesh sieve or nut milk bag into a bowl, squeezing it to release as much juice as possible. Discard the pulp.
Finely grate the lime zest into a small saucepan. Add the sugar and water, and place over medium heat. Stir until the sugar has just dissolved, then remove from the heat and allow to cool to room temperature.
Squeeze the lime juice into the cooled syrup then add the syrup to the watermelon juice. Mix well and pour into the frozen roasting tin. Freeze until partially frozen, about 2 hours, then use a fork to scrape the surface of the granita. The goal is to break up the ice as it forms to create fine shards in the granita. Return to the freezer and repeat the fork-scraping every 2 hours until the mixture is fully frozen in loose shards. Your granita is ready to serve. If you’re not ready, cover and freeze until serving time. If well-covered, it keeps for a week or two in the freezer.