Place one whole cucumber on a cutting board and lightly crush it with the bottom of a pan or pot, using just enough force to crack the flesh and release aroma without destroying structure, then chop it into rough chunks.
Add the crushed cucumber to a large pitcher, pour in the lemon juice, add the honey and the fine sea salt, and stir thoroughly until the honey is completely dissolved and the base tastes bright, clean, and lightly rounded.
Add ice-cold water to bring the total volume to about 3.2 liters, then add the sliced lemons and sliced cucumbers, stir gently once or twice to distribute without bruising, and cover the pitcher.
Refrigerate for at least 1 hour, which is enough for a clean, clear infusion, or let it sit up to 4 hours for deeper flavor, but do not exceed this time or the cucumber will turn vegetal and dull.
Serve well chilled directly from the pitcher, or over ice if preferred, keeping the slices in the water for visual freshness.
