Puree the watermelon in a blender until smooth, then strain through a fine mesh sieve. Bring sugar and 1/2 cup water to a boil in a saucepan over medium-high heat until sugar dissolves, about 5 minutes. Remove from heat. Stir in 3 cups of cold water and the lemon juice. Divide the ice into 12 glasses, and scoop 2 to 3 tablespoons of watermelon puree over the ice, then top with the lemonade. Gently stir before serving.
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