The evidence does not confirm that the 55mm LS is a Schneider design. It is the same optically as the older Mamiya AF 55mm. How do I know? From the absolutely identical optical cross-sections. Attached find the two side by side - I put this comparison together in a couple of minutes; the LS version is a P1 advertisement, and I grabbed the original non-LS AF version from the 645AFD II brochure.
Can you tell the difference? No, neither can I.
Perhaps PhaseOne would like to clarify exactly what role Schneider had in designing this 55mm LS lens? It looks like they merely rubber-stamped the original excellent Mamiya design. Maybe tweaked the coatings.
The other two LS lenses are genuinely new designs, and no doubt Schneider had a direct role in their optical configuration.
Anyhow...there is now a confusing array of M645/Phase lens generations: C, S, N, AF, D, and lastly LS. But not all designs were changed in all generations.
To help disentangle what's what, I've attached some info on the 3 AF wideangles (before the 28mm came along). On the top are my observations regarding these AF designs versus all variants of the old MF lenses (C, S, N). I don't refer to the D or LS lenses in this case.
Ray