Bring 1 cup water and 1 cup sugar to a boil in a medium saucepan. Cool.
Place 4 cups chopped watermelon, 1/2 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.