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Correct lathe height, according to what I've read or heard, is elbow
height for the particular operator. 3/4 MDF sounds insufficient to hold
up a lathe withour vibration, even if it cantilevers the base legs by
only a few inches. You could go with "2" by construction lumber (1
5/8"), tho. I made a whole stand of 2x12 and 2x6 with 3/4 ply sides,
works well and very stable.


Don't need the frame if you glue and fasten the sheet goods. Especially if
you use shelves and/or dividers to reinforce the shell. Think of it as
chipboard monocoque, or "unibody."

Don't need the cantilever if your square cabinet has a larger footprint
than the lathe, and you can gain some good storage as well.

Trouble with construction lumber is folks tend to assemble with fasteners,
which work loose, because full rigid glued tolerances are not met, and the
lumber cycles with RH.