Any permanent habitation should include a smelter to alleviate some of the cost of shipping metals from Earth. From it oxygen or CO2 will be "waste" byproducts, liquefacting and storing them should not be a problem. I can imagine that having large reserve of oxygen will be desired safety feature.

Hydrocarbons will likely be in short supply on the moon but if there is, say, a zinc mined, it could be "burned" in zinc-air cells.

The energy cost of extracting oxygen is higher than you'd get from burning it.

You would extract oxygen during the day and burn it at night

There's also the cost of the diesel fuel (or whatever fuel you burn) to consider. With no native hydrocarbons on the moon, extracting them would be impossible. So they would need to be launched from earth, at many tens of thousands of dollars per kilogram as an ongoing cost.

The biggest challenge to the obvious solutions - either solar plus lots of batteries, or nuclear - would be to crack water into oxygen and hydrogen, and then burn them during the night. The challenge there is storing the hydrogen. But if you do that, basically what you'd be doing is using hydrogen/oxygen as an energy storage mechanism, e.g. as a battery. You'd need to use solar during the day to crack the water.

Why store hydrogen when you can use the metals? I mentioned zinc as that's most mature technology, but almost all of them can be reacted with oxygen to get back energy.

Because the content of metal in lunar soil is very very low.

Not really: https://en.wikipedia.org/wiki/Lunar_soil#Mineralogy_and_comp...

12% by mass is iron, with calcium, aluminum, magnesium at 7-8%. These could be considered ores worth mining on Earth. All four metals readily burn in oxygen, even though aluminum needs some help igniting.

McMurdo used to be nuclear powered, by PM-3A aka Nukey Poo. But diesel was cheaper. On the moon that equation probably reverses.

https://en.wikipedia.org/wiki/Army_Nuclear_Power_Program