When the smoke clears and the dust settles, over levels, the only thing that matters is that the machine cuts straight. I have machines that I purposely run out of level. With small machines, that plastic level would work, for someone experienced in getting a lathe to cut straight. Lets face it, you could set that lathe in your driveway and still use it and cut straight work.
The machine does not have to be level, it has to be straight, and you do not need a level to do that. There are surly some that will disagree, and claim all machinery has to be level or it will not cut properly,,,,,,they get paid good money to carry around those levels. With large, very large machinery, then it is a different matter, and needs special attention. That's way beyond the needs of a gunsmith lathe.
There probably are no small lathes, say under 20" that are perfectly straight, so you may find that getting one perfectly level, might be a chore. and if you do, it probably will not cut straight. Especially with all this cheap iron, that is the rage these days, find one that is straight and a month later it will not be.
BTW I have 3 Starrett 199's...cuz, I don't like moving a level around all day
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.......jackie