Prokudin-Gorskii's images are fascinating, but he didn't use Lippmann plates. Gorskii took three images using red, green and blue filters. That was also much more practical, because I don't think you can reproduce Lippmann plates, while you can print a positive RGB image with CMY(K) dyes. That's why they're CMY after all (cyan absorbs red, magenta absorbs green, yellow absorbs blue).
This is the first I'm hearing about this lack of reproducibility, I can't make sense of it, you could always just take a picture of the resulting plate, no? Except color photos weren't a thing yet, so there just wasn't the technology at the time to make multiple copies?
A the start of the photo era, the state of the art for illustrations was for them to be drawn by an artist and then engraved on a wood block, manually, that was then used as a printing plate. There was a period when no method was available to convert photos to printing plates, so from that period you find prints of photos where someone has manually copied it to a wood engraving for publication.