From the photos it looks like the lathe was designed for a total loss oil lubrication system. Put oil in the oiling points, and it works its way by gravity to where it is needed, and then drips off the bottom of the gears and gear box. I think the grease idea is an effort of the previous owner to stop oil from dripping all over the chip pan, and perhaps to extend the lubrication intervals. The bad thing about grease is that it strongly attracts and holds swarf. Oil also washes out the metal byproducts of wear. If you do decide to go with an oil bath, you will only be able to fill the gearbox to the bottom of the lowest protruding shaft. Oil will have to climb its way up in the box by turning the gears, which gives a sort of a splash/dribble lube system. My Kent 13x40 uses that system, and they recommend way oil in the box to better help to keep the gears and other parts coated between sessions of use. For a drain plug, use a 1/8" or 1/4" pipe plug, square or socket head. Another idea is to use your bottom cover as a drain reservoir only, which would stop the dripping and and keep grit out, and then use the drain plug to let out the excess drippings at intervals you choose, and into a container.