LH/LX spend A LOT of money per passenger in their first class lounges. In fact, they spend more money on food per pax in just the lounge then UA does on an entire TPAC or TATL flight......so its easy to see why they dont want their FC lounges that have only limited space filled with UA passengers (unless of course UA would pay them for this but that aint gonna happen)

Also, UA has a lot of flights out of FRA - can you imagine how busy the FCL and FCT would be if they allowed UA passengers in? It would serve no purpose and really piss off LH passengers. The only problem I have with these rules as a LH passenger - is all these UA flights are code shares. While most UA passengers on UA metal in F are on upgrades or awards, many LH passengers do still buy F tickets, they sometimes end up on UA metal thinking either what the hell, its going to where I need to be OR some dont eve realize its UA metal right away. The F fare is the same for LH and/or UA so LH ends up every day with a bunch of passengers who paid thousands of dollars to LH, for an LH flight only to be told they cant use the lounge cuz they are on a code share. (now that would piss me off royally) There is however a good solution if you are on a non restricted F ticket. just refund it to LH and buy a new one on an LH operated flight.