Concepts for liquefying oxygen (O2) generated from water electrolysis subsystems on the Lunar surface were explored. Concepts for O2 liquefaction units capable of generating 1.38 lb/hr (0.63 kg/hr) liquid oxygen (LOX) were developed. Heat and mass balance calculations for the liquefaction concepts were conducted. Stream properties, duties of radiators, heat exchangers and compressors for the selected concepts were calculated and compared