1 cup (8 fluid ounces) strained fresh-squeezed lemon juice (from about 8 lemons)
4 ounces simple syrup*
3 cups (24 fluid ounces) cold water or sparkling water
2 cups (16 fluid ounces) strained watermelon puree, frozen into cubes
*To make simple syrup, simmer equal parts granulated sugar and cool water for about 2 minutes, or until the sugar has completely dissolved. Do not boil the water, or you will cook the sugar. Sugar in the Raw is my choice for making most simple syrups as it dissolves most completely.
In a large pitcher or blender, place the lemon juice, simple syrup and water, and mix or blend to combine well. Pour the lemonade in a large pitcher and place in the refrigerator to chill.
Place the frozen watermelon cubes in a blender and blend until slushed, adding as much of the lemonade as necessary to blend the cubes.
Pour chilled glasses 3/4 of the way full with lemonade, and top with a few spoonfuls of the watermelon puree. Serve immediately.