You have two YMMV options to get on an LH-coded flight which would (presumably) enable upgrade offers through Lufthansa digital channels:
- Go through the change path on united.com, seeking a similar itinerary. See if they offer LH-coded flight numbers. It happens sometimes.
- Call up United and say you want to upgrade the itinerary but need the flight number adjusted from UA codeshare to LH. Most often an agent will refuse because you're not in the right fare class (PlusPoints from economy to business require
W Q fares and higher). But sometimes it happens; indeed I've been able to do it myself.
Again, these are long-shots, but if you really want to lock something in advance, they're the best I can think of.