I have a Sherline lathe, but I don't think brand really matters for this question.
I mounted the lathe to a 1/2" oak board to provide a base to it. I haven't had any noticeable issues so far, but really haven't done that much work and everything has been small where issues from the board warping wouldn't be terribly noticeable.
I've since come to realize the potential issues of using wood as a base ...
The usual recommendation with machine tools, is to mount 'em through a steel/iron base to a massive concrete
floor. This is because it damps vibrations (and a wood base, though good for support, is just a reflector
of vibrations in metal, it doesn't really carry the sound energy away). So, a stone slab (or some paving blocks)
and a compliant gasket between (lead sheet? Or, maybe just plaster of paris?) would be
good.
Old tool designs used lots of (relatively soft) cast iron, and new ones get computer analyzed with finite-element
models. So, it'll be different depending on the tool, and its use. Variable speed motor schemes
are a trifle scary, there will be some potential for a VFD to hit a mechanical resonance, and cut
quality can suffer. A single-phase motor mounted on the lathe (instead of belt-coupled) could make
a lot of 120 Hz torque variation, too. It seems counterintuitive, but an oak board could just
become a spring in an oscillating mass/spring system.
BG Micro has the right gizmo for sale, if you want to find and snuff vibrations, though:
<
http://www.bgmicro.com/search.aspx?find=seismometer>. I bought one, plan to
wire it up and explore when I also get a round tuit...