Wash 1 large cucumber thoroughly and chop it into small pieces.
In a blender, add the chopped cucumber, juice of 2 lemons, 3 tablespoons of sugar, and 1 cup of water. Blend until smooth.
Strain the mixture using a fine mesh sieve to remove the pulp, collecting the liquid in a large pitcher.
Add another 2 cups of cold water to the pitcher and stir well.
Taste and adjust the sweetness by adding more sugar if needed.
Add a few mint leaves for an extra refreshing flavor and stir again.
Chill in the refrigerator for at least 1 hour.
Serve over ice cubes in glasses, garnished with lemon slices and mint leaves.