Install older version of Lightroom. Is it possible?

Modern computers need modern software that's compatible.

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following for both Windows & Mac.

• Photoshop CC and Photoshop on iPad
• Camera Raw
• Lightroom on desktop, mobile and the web
• Lightroom Classic (similar to LR 6)
  
• Portfolio website + hosting
• Adobe Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).
• Free upgrades for paid subscribers

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

Make sure your computer meets the minimum CPU & GPU requirements. Most Creative Cloud apps work on:

• Windows 11 (64-bit), Windows 10 versions 21H2, 21H1, 20H2;
• macOS 12 (Monterey), macOS 11 (Big Sur), macOS 10.16 or 10.15 (Catalina).

- https://helpx.adobe.com/creative-cloud/system-requirements.html
- https://helpx.adobe.com/lightroom-classic/system-requirements.html

Hope that helps.

you can install older versions if you have a compatible os and a license.

that said, you have a new mac with what os version?