Originally Posted by Kacee

You cannot upgrade through United.

I upgraded a UA ticketed, LX operated and coded flight from P to A in December via the LX website. It was pricey but a very nice experience. The F seat is sooo much better than the J seat. We had no issues with the ticketing. Note that I'm talking about a purchased LX upgrade, NOT an upfare (which would be prohibitively expensive).

I don't see a reference in the OP to the LX segment being a codeshare.