Bring I cup water and 1 cup sugar to a boil in a medium saucepan. Cool. Place 4 cups chopped watermelon, ½ cups chopped strawberries, and the juice of 4 lemons in a blender. Add the cooled sugar water. Blend on high speed until the fruit is pureed. Pour into a pitcher and chill. Serve over ice or with sparkling water. Serves 8.