As FYI, you have to call LH to change/select seats, or at least I did. This really drove me crazy because I know I've gone to Lufthansa.com to assign my seat in the past.
Many of the routes I looked had one or more LH codeshare segments on these UA flights, so I guessing there are many of us in the same boat. Found several 'work arounds' talked about in forums, but none of them worked. The phone agent told me they know the website is broken.