Combine half of the watermelon, half of the water and half of the sugar in a large food processor and pulse until liquid. Transfer mixture to a strainer and strain the mixture into a large container and disregard anything that won't strain. Repeat process with the remaining watermelon, water and sugar. Once the entire mixture has been strained, ad the lime juice and refrigerate for at least 2 hours.

When ready to serve, add a lime wedge if desired and just a splash of Sparkling water.