Cucumber Lemonade

Thinly slice 1 cucumber and 1 lemon to measure 1/3 cup slices each; set both aside for garnish.

Coarsely chop the remaining cucumber to yield about 3 cups; place in a medium bowl. Juice the remaining lemons to yield 1 cup juice. Add the juice to the bowl with the chopped cucumber. Add sugar and mint; stir to combine. Cover and refrigerate, stirring occasionally, until the mixture is chilled and the sugar dissolves, about 30 minutes.

Pour the cucumber mixture into a blender and blend until smooth, about 20 seconds. Add 1 cup water and blend again. Strain through a fine-mesh sieve into a pitcher; discard solids. Stir the remaining 3 cups water into the pitcher and garnish with the reserved cucumber and lemon slices. Serve over ice.