In the work bowl of a food processor, process watermelon until smooth. Strain through a fine sieve, reserving 4 cups juice. Discard solids.
In a small saucepan, combine water and sugar. Bring to a boil, and boil for 3 minutes or until sugar dissolves. Let cool completely.
In a large bowl, combine reserved watermelon juice, simple syrup and lime juice. Pour into a 13x9-inch baking pan, and place in freezer. Freeze for 6 hours or until no liquid remains, scraping with a fork every 2 hours.