Unable to reinstall Lightroom Classic after Adobe suggested I uninstall it

You own a license; not the software.  Adobe owns the software and they can discontinue it anytime.

Assuming your computer supports legacy products, you can try the installer links on Pro Design Tools.  Make sure to follow the VERY IMPORTANT INSTRUCTIONS otherwise Adobe's servers will error out and you won't get access to the file(s).

Given Lightroom 6's advanced age and lack of support for modern equipment, you might be better off getting a subscription to Adobe's Photography Plan.

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Lightroom on desktop, mobile and the web
• Lightroom Classic (similar to LR 6)
• Portfolio website + hosting
• Creative Cloud Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).

https://www.adobe.com/creativecloud/photography.html

Hope that helps.

So if you do not have a subscription to a Photography Plan, then you do not have Lightroom-Classic.

So which Version Number of Lightroom do you have?

(And you cannot just "buy" Lightroom any more.)

Please include the following in your question:
Adobe product, exact name, and Version number.
(If available: A Screenshot of the info panel from MENU: Help/System Info...)
Computer Operating system and Version number
The full text of any Error Message(s)
What you were doing when the problem occurred.
Screenshots of the problem.