Yes - Lightroom 6.14 runs ok with Mojave. It's actually a 64-bit app, but it has various 32-bit appendages, including the installer, uninstaller and updater.
NOTE: All of those bits will not work on Catalina, and people have noted that in Catalina, they can't quit and had to force quit - which eventually corrupts the database. Someone has reported that removing all the 32-bit parts in Catalina did allow one to quit the app normally, so that may be the way forward. However, there may be other issues - I'm on Mojave on the laptop and still on High Sierra on the iMac, because I can't afford the time to deal with moving 100,000+ images into a new app (CaptureOne - which doesn't work entirely in Catalina yet, either) or concede defeat and subscribe to LR/PS (neither of which are yet entirely compatible with Catalina either as of this writing).