In a blender, blend the chopped cucumbers until smooth.
Strain the cucumber puree through a fine mesh seive into a pitcher, pressing on the solids to extract as much liquid as possible.
To the cucumber juice in the pitcher, add the fresh lemon juice, sugar and cold water.
Stir well until the sugar is completely dissolved.
Taste and adjust sweetness if necessary.
Add ice cubes to the pitcher and stir again.
For the best flavour, let the lemonade chill in the refrigerator for atleast 1 hour.
Serve the cucumber lemonade over ice.
Garnish with thin slices of cucumber and lemon.