Place watermelon in a blender. Cover; blend until smooth. Pour puree into a pitcher and keep very cold, even a little frozen to make it icy.
For two martinis, add one cup of watermelon puree, 1/4 cup of lemon vodka, two tablespoons of lime juice, one tablespoon each of Cointreau and sugar to the blender with three to six ice cubes. Cover; blend until slushy. Makes 6 large martinis.
