Lightroom 6 only runs under 64 bit operating systems. It cannot be running on a 32bit operating system.
apple is telling me Adobe needs to upgrade
I have no idea what this means.
If you really have Lightroom 6 and it is running on your Mac, then Lightroom is running 64 bit and no upgrade should be necessary.
Please see the screen shot below.
I have no idea for MAC, and I may be wrong for Windows as to LR 6, But way back, when I had LR 6 on Windows, I think both 32 and 64 bit were installed. (or was that prior v6) This may have changed between v 6 and v6.whatever.
Now in Windows, a "Program Files" and a "Program Files (c86)" folder exist and the 64 bit copy would be in the former.
As to MAC? no clue. and the 32 bit LR support in MAC may have ended (on Adobe end) prior to the 32 bit ending in Windows.
In your Apps folder, make sure that a second Lightroom app (64 bit) does not exist (would think a MAC would default to that if it did).
Oh, and if your OS is Mojave, pay attention to all the issues members are having.