I had a recent catastrophic loss and had to replace my Mac. Adobe no longer supports the downloadable installation of LR6 and their customer service rep advised I check on the forums. My new computer does not have an optical drive, so I would need support online.
To be clear for the OP and others in this situation, one can end up running LR5 and LR6 off Catalina, Big Sur or Monterey, it is the install process that takes a little work. With a simple hack (its not even a hack); boot off an older OS, install either, now you can run, with some limitations, those products under Catalina, Big Sur or Monterey.
No, I don't recommend doing so, but it is doable.
Author “Color Management for Photographers" & "Photoshop CC Color Management"