I understand now about the baggage allowance when using a Star Alliance partner airline like LH from UA. But consider the following excerpt from the UA Mileage Plus web site.
Premier® members, and up to eight companions booked under the same confirmation number as a Premier member, are allowed two standard-sized checked bags, up to 50 lbs. each, without baggage charges. (There is no language anywhere on this page that says this is only for flights on United. It would have been easy for them to add "when flying on United, United Express, etc.," but they didn't!)
Premier members also receive Star Alliance Silver benefits when flying on any Star Alliance member.
Star Alliance Silver and Star Alliance Gold status provides additional recognition and rewards across all the member airlines...(In addition to your Priemier status benefits, right? Or at least that's what it appears to say.)
The emphasis is mine. I believe that a reasonable person could construe all this to mean that 1) you are allowed two pieces of baggage, 50 lbs each, and 2) the Star Alliance benefits are in addition to ("also" and "additional") your Premier status benefits when flying on partner airlines. I'm not saying this is the actual benefit, but at best the above excerpts could be called misleading, even if unintentionally.
And then there is that other reference in my earlier post about three bags instead of two for Gold status, which pretty strongly implies that Silver status allows two bags.
Add to the confusion that I actually purchased the tickets for these flights from United. I made what I thought was a good-faith effort to understand the rules, but was misled by this sloppy language. Once I got to the airport, I had no other choice but to pay up.