[Arran]

I would try the lacquer on the side first in a test area, like Mr. Douglas mentioned, see if anything bubbles or whether it sticks or not, my guess is that they used some sort of paste varnish over top of hardware store oil stain. Knowing from experience you will likely need to strip the sides and top, I haven't had much luck spraying lacquer over anything but lacquer and sometimes shellac. It would be fairly simple to cover the front panel, polyethylene vapor barrier (6 mill) held on by a double layer of masking tape around the edges. When using the stripper use an artist's brush and a razor blade to strip it around the edges of the front panel so you can control where the stripper goes. When you have finished stripping use a hair dryer to warm up the tape before removing it so it doesn't pull the finish off the front panel.
With regard to the flaking finishes on the tops and sides of these set there could be any number of reasons for it. The bulk of the cabinet appears to be made out of one piece of laminated poplar, what's more the grain of the top layer runs from back to front so expansion and contraction could be a culprit, if the wood was contaminated there would be one production run with the flaking finish but not the majority. I'm thinking that it must have been a poor quality brand of shaded lacquer, the previous arched model 16B cabinets and many of the consoles seem to have this same flaking problem on the shaded portions; or it could have been a poor quality sealer, early 90's G.M cars had a problem with a bad batch of primer causing flaking paint.
Best Regards
Arran