Mac High Sierra 10.13.6 not compatible with Lightroom C

There are ways to get higher OS versions via patchers from Dosdude1. Disclaimer: Entirely unofficial, so the call to try it is yours and yours alone. I had Mojave on a 2008 Mac Pro. Catalina is the highest though. Just google 'dosdude1' and decide if it's worth a try. 

see:

(ref 1): Lightroom Classic system requirements | earlier releases | Adobe

from (ref 1) you can look at the system requirements for previous LrC versions (pre v12)

I think that you will find that you are limited to LrC v9

(ref 2): Lightroom Classic 9.x system requirements | Adobe

while LrC v10, is a no go

(ref 3): Lightroom Classic system requirements (v10) | Adobe

Now, next issue is how to download v9. The Adobe Creative Cloud Desktop App, normally only shows the last two versions. But, I am not sure if it will note that neither version is available for your OS and be nice and show you v9.

Following from another posting, relates to how to install older version

"You have to contact the Adobe support and ask for an download link for the appropriate version of Lightroom.

Contact Customer Care (adobe.com)

Click on the Chat icon at the lower right. If asked, choose the “Download & Install” category, or type in "agent" to get a human and not the chat bot." credit: Axel Matt

from: https://community.adobe.com/t5/lightroom-classic-discussions/older-version-of-lightroom-10-x-for-osx/m-p/13316648