A method for estimating the mass and fission surface power requirements of a lunar oxygen production facility is introduced. The individual modeling components involve the chemical processing and cryogenic storage subsystems needed to process a beneficiated regolith stream into liquid oxygen via ilmenite reduction. The power can be supplied from one of six different fission reactor-converter systems. A baseline system analysis, capable of producing 15 tonnes/yr of oxygen, is presented. The influence of reactor-converter choice was seen to have a small but measurable impact on the system configuration and performance. Finally, the mission concept of operations can have a substantial impact upon individual component size and power requirements.