Lightroom 6 not compatible with my Mac

The only alternative Lightroom products that can run on current MacOS systems both require an Adobe subscription (basic cost is $9.99 per month). Lightroom Classic is the updated version of the LR6 that you were using (currently at version 12), and there is the much newer cloud-centric version called simply Lightroom.

EDIT: Perhaps you could clarify which version of "Lightroom 6" you are referring to? The "old" Lightroom 6, or the newer cloud centric Lightroom, which is currently at version 6? Neither can be installed on MacOS Catalina, the older Lightroom 6 because in that case the MacOS version is too new, and the newer Lightroom 6 because the MacOS version is too old! There's no fix for the older Lightroom 6 (unless you downgrade the MacOS version to Mojave), but the new Lightroom 6 could be installed if the MacOS version was updated to Big Sur (or later).

There are of course non-Adobe alternatives such as Capture One and ON1.