1. Add lime juice, lemon juice, and sugar to a pitcher and whisk together until the sugar is dissolved. 2. Place 4 cups of watermelon, cucumber, and ginger in a blender. 3. Pour watermelon mixture into a fine-mesh strainer placed over the pitcher. 4. Add water, the remaining cup of cubed watermelon, and a few slices of cucumber to the pitcher as well, and give everything another stir.