Can't use Lightroom Classic without internet

It is necessary to connect the PC to the Internet when installing.
If the license authentication passes, you don't need to be connected to the Internet all the time when using it.
If you haven't been online for a while, you'll need to reactivate your license.

See https://helpx.adobe.com/creative-cloud/kb/internet-connection-creative-cloud-apps.html

You can work offline for up to 129 days.

If you plan to work offline for some time, do not sign out. With no Internet, you won't be able to sign back in.

It's good practice to always be signed in.