He wasn't trying to travel to Germany, rather just via Germany.

There wouldn't have been any passport check in German at all.

It's simply that Schengen does require some Nationalities to have a Visa (in most cases they'll get a Transit Visa, OP's friend had a full Visa which does just work as well for that) even when just transiting. I assume this is for "protection" against claiming Asylum status when they get to Europe for their transit.

However, as Germany decided having "mandatory signature" in their passport rule, OP's friend couldn't board. Technically, again, Lufthansa was all correct - OP needed a valid passport for travel as "stated by Germany", even if the German immigration/border police wasn't going to be checking his passport (as he wasn't going to enter Schengen)

The problem here isn't with Lufthansa - but with German overstrictness of, lets be honest, rather unique rules, even when they wouldn't even have a look as his passport in Germany (Staying in Transit) AND him having the Visa to do so.

Was it correct from LH to block OP's friend from boarding? Yes
Could they have made an exemption? Probably yes, especially given the situation.

Imho, if LH wanted to be customer-friendly, they should have re-routed OP through ZRH. Would have been totally possible as well (afaik, similar flight times)

But we know that LH doesn't try too hard to be customer friendly. They like to play exactly according to the book. Which means here, from Lufthansa's point of view:

Passport without signature is not valid for any travel to/via Germany, no matter what. You're on your own, we don't care.