Out of curiosity, how does one actively use Google flights to bring LH-coded flights into united.com? Certainly, one can use Google Flights to deep-link to united.com so that an itinerary can be purchased through United and therefore issued as a 016 ticket, but in my experience the flight numbers will be UA-coded if that's how UA would otherwise market the itinerary. It's kind of like what you say about the change path - usually does not happen, but absolutely can and does happen. If there's a trick to forcing native LH flight numbers from the get-go, that'd be great.

In any case, calling can clear it up after booking.