Is there some sort of conservation of energy question in this form of water collection that establishes some minimum amount of energy that would be required to collect 1L of water from the air?
I'd assume if the amount of energy required to collect the water is low then we're looking at something interesting.
Yes, water vapor condensing to liquid water at humidity below 100% is an exothermic reaction, and the amount of energy released is (per Google) 2259kJ/kg. So any device that wants to condense 1kg of water has to dissipate at least 2259kJ of energy somewhere, assuming it is in any way temperature-dependent (if it can keep condensing water even if it becomes hotter, then this is somewhat evaded).
For context, that amount of heat is five times the amount needed to heat 1kg of liquid water from 0° to 100°C (without thawing or boiling it). So it's not in any way a trivial amount.