Place chopped cucumbers in the blender with 1 to 2 cups of the water. Strain through a fine mesh sieve into a bowl or into the pitcher, pressing with the back of a ladle to get all of the juice through the sieve. Discard pulp. Add ice on top of cucumber.
Heat 1-1/2 cups of the water on a stove top over high heat until steaming, but not boiling. Remove from heat and whisk in honey until dissolved.
Pour honey mixture, lemon, and water over ice and cucumber. Stir well to combine. Enjoy!