Make a simple syrup by stirring the water and sugar together in a saucepan over medium heat. Heat until just about to boil and the sugar has dissolved. Place in refrigerator 30 minutes, or until cool.
Place the cucumber slices in a blender or food processor; blend until mashed into a pulp.
Pour the cucumber pulp into a fine mesh strainer place over a bowl to catch the liquid; allow to sit until you have about 2/3 cup of liquid from the cucumber, about 15 minutes.
In a pitcher, stir the simple syrup, cucumber liquid, and lemon juice together. Add more water depending on your taste preference. You may also add the cucumber pulps.