Yes we all agree that the steam condenses in the lubricator vessel and it is this that displaces the oil. My apologies if I misled by not saying that I agreed with this basic principle at the start.
Our discussion is whether this Simple Displacement Lubricator might be a continuous system or a cyclic one. This lubricator uses the same entrance and exit to the steam line, or steam chest as fitted by Stuart. I suggest that the flow direction must cycle. An experiment would be simple to do – just connect a steam line to it and leave it under pressure, and see if it gradually fills with water and all the oil transfers to the steam line.
There is another configuration sometimes called the Hydrostatic or Ramsbottom style that has a steam inlet, typically from the regulator supply, to the displacement vessel and a separate oil outlet to the cylinders. These do not need to cycle and are effectively continuous. They were developed for use on full size steam locomotives and even included sight glasses to observe the dripping oil flow. If configured to take some steam directly from the boiler they would then operate continuously. They are still used on some model locomotives, especially GWR variants.