"Priority Boarding**
As a Star Alliance Gold member, you will be able to enjoy the freedom of boarding at your leisure. That's because you are entitled to board at your convenience along with First and Business Class passengers and other top-tier frequent flyer members.

**Where available"

from "Benefits - Star Alliance Gold Benefits - www.star-alliance.com

If LH has fully informed this I'd say they're partially waived from guilt; Nevertheless they should explicitly write it in the Star-Alliance web-site, where *A customers get the rules from.

One is not expected to know the details a specific carrier has implemented changing the major rules of the alliance they belong to, by writing in some documents...

By the way, Mexicana fully complies, which I guess leaves us with LH not complying ?

Sorry Rudi, but this is my opinion; I never flew LH and I'd expect to be given priority boarding. Thanks for your info, nevertheless.