Hmmm an interesting question... not too sure on the legal standpoint as technically the cabin space is private property. In theory, with permission from the airline reps (cabin crew etc..) it should be allowable.
The CSS probably demanded the images were removed to keep the peace, so to speak... they cannot force you to delete your photos.. (although they can appropriate your camera for the duration of the flight if, in their eyes, you are flouting airline safety regs.. could be used to justify a hell of a lot ): )
The pax was within his rights to
request the removal of said photographs, however simply showing him that they were not of him should have calmed the situation, unless of course they were of him
As for him threatening to sue

)

) that would be an entertaining (and quickly dismissed) lawsuit...
Aircraft - private space owned by airline.
Airport - private/public dependant on the holding company of the land and buildings.... depends in which country too as there are nationalised airports and landing strips out there.
Airline lounges are an interesting one... in rights they belong to the company leasing the space from whomever holds the airport freehold, however I would not be surprised if there were clauses buried in lease documents making both parties responsible for some types of legal entanglements or may even shift the blame to one another ii)
Hope this helps 8D