Add the cucumber slices to bottom of a pitcher. Use a wooden spoon to lightly muddle (mash) them several times to release the juices.
Add the cold water. Refrigerate for at least 1 hour before serving (you can add fresh mint sprigs if desired). Flavor is best within 1 day, but you can store up to 3 days refrigerated. Serve with lemon slices if desired. Or, add a splash of sparkling water.