[edited per comments]
Recall that these kinds of "motion picture cards" have been around for decades; at least 40 or 50 years, maybe longer. If such a camera (or even a home-based process) could have been built for consumer use, it probably would have been sold. The fact that it wasn't, and the fact that even during all these years there haven't been many manufacturers of such images, should give you an idea of how difficult registration of the image stripes with the lens can be. A purely mechanical process (printing the image onto some kind of paper, then laminating the lens over the top) probably can't be easily (or cheaply) done - otherwise it likely would have been.
That's just my take on things, of course; maybe I'm completely wrong, or there's some method or such I am missing that could make the system easier to build today? I do think the idea of "reverse printing" might be a step toward it. I can't think of how you'd build such a thing to be hand-held, but I can imagine a desktop-sized machine being potentially possible (again, using some kind of close-imaging camera or some other method to register the printing of the images with the individual lenses on the plastic).
It'd also be reusable!