For the simple syrup: Bring the sugar, lemon zest and 1 cup water to a boil in a small saucepot. Allow to simmer until the sugar is completely dissolved, about 5 minutes. Strain through a fine-mesh strainer and stir in the lemon juice. Allow to cool to room temperature, then refrigerate to chill for at least 1 hour.
For the bug juice: Place the cherries in a blender with the lemon simple syrup. Blend on high speed until the cherries are completely pulverized. Pour the mixture through a fine-mesh strainer.
Combine the cherry juice with 3 cups water in a large pitcher. Serve over ice.