Just anecdotally, on two separate trips last fall Lufthansa was offering $400-500 USD upgrades to business class LAX-FRA. Granted, this was their rather tired 2-2-2 cabin on the 747-8 (upper deck is 2-2 but was full), but I felt the value was pretty great. I paid on the overnight outbounds and just lived with Y on the returns since it's a daytime flight. Should be possible to get a (LAX/SFO/SEA)-FRA-LHR routing but I haven't checked.

Definitely not guaranteed that you will see a reasonable upgrade rate, however, and I don't have any more recent data points.