Making liquid oxygen (as opposed to gaseous oxygen) is not a terribly efficient process.
You have to do the trade between liquefaction and storing oxygen as a pressurized gas. Reusing a single Starship's propellant tanks, for example, at 6 bar would hold ~14 metric tons of oxygen, enabling a continuous lunar population of over 1,000 people.
The compression or liquefaction energy isn't a show-stopper necessarily, it just works into the total energy efficiency of the storage system. Compression is nice because practical isothermal compressors are now being demonstrated.[0]
Both liquefaction and compression require cooling. I do think it probably makes sense to do the thermal storage trick in reverse also, storing up a bank of "cold" at night to be used during the day. The thermal radiator panels still provide (derated) cooling in the day, but the thermal storage pool time-shifts the natural oversupply of cooling power at night.
[0] https://newatlas.com/good-thinking/carnot-centrifugal-air-co...
...which is why you want to be extra careful in how mass-efficiently you're storing it.
A tank of liquid oxygen masses only a few percent of its contents, and its contents store more chemical energy per mass than a lithium battery. Later on, insulated tanks are vastly easier to produce from lunar materials vs batteries. These are all nice leverage multipliers.
Nuclear is a popular notion, but the real-world economics don't favor it. Effectiveness beats elegance.[0]
[0] https://spacecraft.ssl.umd.edu/akins_laws.html