Why is Adobe Lightroom 6 incompatible with the upcoming macOS 10.15 (Catalina)? I receive a system warning that Adobe Lightroom 6.14 (perpetual license) is incompatible with future versions of macOS when starting it under macOS Mojave. Lightroom 6 is a 64 bit application, so where is the incompatibility?
Catalina drops support for more than just 32bit apps. Kernel Extensions are no longer supported for example. If Lightroom uses a kext, this will not work. Catalina also runs the system from a read only volume. If Lightroom requires modifying any of these folders, then you're out of luck.

However, I don't believe the above is the cause. Correct me if I'm wrong, but Lightroom 6 (what you're using) is Lightroom CC (2015) or earlier right? If that's the case, the last time I used Lightroom CC (2015) the main app is 64bit but parts of the app are 32bit. A quick search online suggests that the parts in LR that are 32bit include Adobe QT32 Server and dynamiclinkmanager.

I've not tested it, but I suppose there is a small chance that the app could run without these 32bit components. Maybe I should stop speculating.