8 cups seeded watermelon cut into 1-inch chunks
1 cup hulled and quartered fresh strawberries
1 cup granulated sugar
1/2 cup freshly squeezed lemon juice (about 3 lemons)
2 cups water (approximately)
Thin watermelon wedges with the rind (optional)
In a food processor fitted with a steel blade, pulse the watermelon, strawberries, and sugar until blended and smooth.
Strain through a fine-mesh strainer into a 2-quart container, pushing down on the solids to get all the juice. Add the lemon juice and enough of the water to make 1 1/2 quarts.
Chill until very cold. Serve over ice with a wedge of watermelon, if desired.