Add lime juice and sugar to a blender. Then add some of the watermelon, until your blender is ¾ full. Blend all the ingredients until smooth. Pour about half of the mixture into a rectangular baking pan. Add your next batch of watermelon and blend again. Pour into the dish and give it a mix.

Freeze the mixture uncovered for 1 to 1 1/2 hours. Stir, mashing any frozen parts with a fork. Freeze mixture until firm, about 2 hours. Scrape granita vigorously again to form icy flakes. Cover tightly with foil and keep frozen. Give it a quick scrape before serving. Every freezer is different so your freezing times may vary. Basically freeze and scrape, freeze and scrape. But do yourself a favor and don't check it too often or it will take too long.

Use any leftover watermelon to scoop out chunks with a melon baller to add to your granita. Garnish with lime slices and thin mini slices of watermelon.