Will Adobe Lightroom 6.14 work properly with an iMac with with OS Ventura?

What model and year is your iMac and what system are you currently running? If it's 10.14, Mojave, I doubt if that version of Adobe Lightroom will work on Ventura because beginning with 10.15, Catalina, all apps must be 64 bit. You can download the free app GO64 and it will tell you which of your apps are 32 big and will have to be upgraded or replaced with an alternative.

Yes, the 2017 iMac can run Ventura. I have a 2017 iMac and am currently running Ventura.

Just a note: if you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac they should be uninstalled according to the developer's instructions before upgrading. They are unnecessary and can only hinder system and application performance.

Adobe ended support for Lightroom 6.x back in 2017 and as of the end of 2023 it can no longer even be downloaded from Adobe.

The last version of macOS that LR6 was qualified on was High Sierra (10.13.6) although it will run on macOS Mojave (10.14) ... but not Catalina (10.15) or later because LR6 is "32bit" software. Starting with macOS Catalina, all apps must be 64bit software.

Adobe Lightroom 6.14 is compatible with macOS Sierra (10.12) through macOS Mojave (10.14). However, compatibility with macOS Ventura isn't confirmed as my data is only up to January 2022. For the most accurate information, visit Adobe's website or contact their support team.

It won't run. While the app is 64bit the licensing and verification code is 32bit so there's no way to register the app and so it won't install.