What a weird predicament! I don't believe adding the suffix -3 is going to make any difference. It is in the name of the file that determines whether the catalog needs to be updated. It's the basic structure of the catalog itself. Are you sure that the catalog with the -2 is one that was updated with the new Lightroom? Or could it possibly be a carryover from when you updated the first time in Lightroom 5? I know, it's a dumb question. But what you are experiencing doesn't make sense.
Does the LR catalog folder contain both the updated LR CC FILENAME-2 catalog file and the original LR 5 FILENAME catalog file? If so try "moving" the original LR 5 FILENAME catalog file to another folder.
I have managed to upgrade to LR CC on the Air, but, when trying to use it for the first time it has said that the catalog needs to be upgraded, and it says it will create another new version of the catalog, with the suffix "-3".
First question: Why is it saying that it needs to upgrade the catalog "for use with Lightroom 6", when it is LR CC I have? Is it because functionally LR 6 and LR CC are basically the same, so I don't need to worry about that?
Are you sure LR CC and NOT LR 6 are installed on the MacBook Air? From inside LR go to Help> About. What do you see? It should say 'Adobe Photoshop Lightroom CC.' If so try my suggestion and report back the results. Thank you!
Thank you both for your suggestions and apologies for taking so long to reply. Real life issues have taken precedence the last couple of days!
Well, hopefully the problem has gone away. I started LR on the MacBook without the portable HDD plugged in and I told it to create a default (empty) catalog, which it did.
I then plugged in the portable and said I wanted to load an existing catalog. I pointed LR to the -2 version and it just loaded it up without asking any questions about upgrading.
BTW, I did check and it is definitely LR CC on both machines, not LR 6.