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.
LR 6 and 5 are not compatible due to the installer that is 32 bit. Even Adobe indicates that previously installed versions will likely continue to work. But you will not be able to install on a fresh install. Perhaps the installation steps can be replicated, the activation would probably be the most complex.