I would think that one of the problems with a spindle lathe would be that the piece would have to be symmetrically straight like a baseball bat or a table leg. A lathe would not be able to cut eyes, fins, a lip...or even have a tail curving down.
I have made some lures with a 3D printer (straight PLA) and was not happy with the result. First of all, sanding PLA cant be good for the lungs. It's defiantly harder than wood. I have had some latches I made pretty much just break after a year of so outside (UV). I probably should have use something other than PLA. 3D printing is a little new to me so Im sure there is something about it I'm missing.
I do know they make a wood filament that 70%PLA and 30% wood derivative (haven't use it).
I do think eventually 3D lure making will be popular.