This is what the Swiss First Class on the A340 looks like:
As for the question in ZRH: Are you allowed to enter Switzerland? If yes then there is no issue with going to the F lounge for breakfast. I believe the arrival service is available again, so you'll be picked up at the plane and driven to the private passport and security check, from which you can then enter the A F lounge. Not sure if they serve eggs Benedict atm, but would recommend those for breakfast. After that you can go in to the city and then return later and visit the F lounge again before your connection. Just make sure you keep your arriving F boarding pass for entry.
As for the 5:30 arrival time, flights only land from 6 am onward, the earliest you'll be out of the airport would be 6:30.

What partner special are you booking? The LHR one?