I'm fairly certain that by level they actually mean that the bed is flat and straight, without any twist, also that the centerline of the head stock is parallell to the flat staright bed, inboth the horizontal and vertical plane.The tail stock should also be on the same centerline. I spent most of my adult working life as a Marine Engineer
Without exception the shi[ps I worked on all had a lathe in the engineroom workshop. Some also had other machines as well. The sizes varied from about 9 inch to about 14 inch swing with beds from about 3 ft to 6 ft longt, mainly depending on the size of the work that was anticipated.
These machines were usually bolted to a substantial steel sub frame that was made to be quite square. the sub frame as then resiliently mounted to the ships frame, so that as the ship flexed the lathe on its sub frame remained quite rigid, square and straight.
I always found tthat it was possible to do quite accurate and detailed work on those machines, except in extremely rough weather.
I can only recall one case where the lathe was pretty useless while the ship was at sea and in that case the above procedure had not been followed.