Simply: It doesn't matter, but the steam supply line is hotter so the steam oil is partly vaporised or lower viscosity. But the engine demand causes oscillations in pressure of the supply line anyway, so these oscillations contribute to the various factors that cause the oil to come out of the lubricator - replaced by steam (which condenses to displace oil). So "without valves", the displacement lubricator actually "pumps" the oil out of the lubricator. Some very complex gas modelling software should be able to model this. All you need to know is that providing there is a pumping oscillation of the steam where the lubricator is connected, then you'll get oil. So the valve chest (inlet side, NOT exhaust!) is good.
Don't worry about the slide getting oil everywhere. Oil will creep across all surfaces for lubrication. In the cylinder, vaporised oil (if the steam is hot enough) actually condenses before the steam forming microscopic droplets (aerosols) that then form nuclei for the formation of the water droplets that form as the steam is cooled by expansion in the cylinder (losing heat as work on the piston). The oil droplets also condense on cylinder walls, etc. So the Wet steam is actually a water-oil emulsion, made in the cylinders. Good to wash this out after a steaming session with liberal WD40 before lubricating the engine completely. I use motor 7W30 engine oil (as it has good corrosion inhibitors) for leaving the engine ready for another day. (Oil technology is a science, not a "crude" subject! - The use of appropriate oils is good engineering). But only use STEAM OIL in the lubricator. - The engine oil will soon be displaced upon pre-steaming barring with steam to warm the cylinders, when the displacement lubricator is priming (heating-up and pressurising) before supplying oil.
K2