Cucumber slices, lemon wedges, and mint leavesfor garnish
Combine the cucumber, lemon juice, mint leaves, and honey in a blender. Blender until smooth, adding some water as needed to promote blending.
Place a mesh sieve over a pitcher. Pour the cucumber mixture through the sieve. Use a wooden spoon to push down the mixture to squeeze out all of the juice as needed. Remove the sieve and discard the pulpy mixture.
Stir in about 4 cups of water, taste, and add more as desired. You could also use sparkling water. Serve over ice with garnishes.
Keep in a covered pitcher in the fridge for up to 5 days. Stir well before serving.