The codeshare and natural LH flights don't share fare filings or inventory buckets. There is some overlap for inventory control to make sure the seats exist, i.e. LH isn't going to release premium economy fare space to UA on the codeshare unless there are physical premium economy seats available. But otherwise fare bucket inventory is semi-independent. I.e. If R bucket space is released to the UA codeshare, then a UA R fare filing can fill it. For all intents, at this stage in the process, the flights are being sold as two separate things, sure a booking on one may affect the fare bucket inventory on the other, Since this is TATL, who you book with is revenue neutral for both UA and LH, the fare is split between them regardless if its the UA or LH flight number (though obviously they both make more if you unwittingly book the higher priced LH fare).

In just when your already confused about airline pricing. How about this, the return to JFK has the fully refundable fare cheaper than the restricted ones.