Even if the OP's hypothetical passenger doesn't intend on flying LH, if they intend to fly to European destinations, then Star Gold access to the LH Senator lounges above the Business lounges upon transfers in Europe and departures from Europe is a nice benefit. In some cases, a very nice benefit.

Even for US departures, in cases where Polaris lounges are not constructed or closed, but LH lounges are available, Star Gold provides access that paid UA business class wouldn't. Access to US domestic TK lounges (something I've not tried myself) has been reported to be valuable as well.

In popular outpost airports (for me, the primary instance is Santorini), where business class seating is not offered and there are serious crowds, you can still get priority check-in with Star Gold status. Sometimes it takes a quiet inquiry to a side office in order to be escorted to the front of the line with an, "of course, sir, this way please, sir." (To the naysayers on JTR: Only very recently has A3 offered business class on ATH-JTR flights, and it isn't clear that will continue.)

And, to the OP's hypothetical passenger, I might suggest that while the consensus on this forum is that UA's Polaris service is somewhat superior to LH's business class, the intricacies of flight schedules and supported routes can make LH's service the more convenient choice. I doubt many of us here would refuse to fly if the only option were LH business class. Or SWISS's business class for that matter.

I'm sure someone more familiar with UA's service to Asia than me can fill us in on the equivalent assertions for trans-Pacific flights.