In a pitcher, mix the water, cucumber, 3 mint sprigs and lemon. Let it rest on the fridge for 24 hours. If you prepare the water at the last minute, cut the first cucumber in three or four pieces. Then, squeeze the cucumber pieces to release all the juice.
Before serving remove the cucumber slices used to flavor the water. Then stir with a wooden spoon, add some ice cubes, 6 or 7 fresh cucumber slices and the remaining 2 mint sprigs. Now enjoy!