Lightroom Classic not responding

Also, Windows Task Manager, what is show.

With LrC running:

With LrC closed (and I made sure that lock file was gone before bringing up the Task Manager)

Up in the top screen capture,  that be the case, you can try stopping that app (right click, end task) in the Tasks Manager. (and see what happens)

Have you restarted your computer? A restart not a shutdown (due to fast startup on a Windows 10 or newer)

A restart should close open services, apps, etc, a shutdown might restart them upon boot.

Point is to see if a restart will flush out something that is not closing properly.

Actually looking at your attached images this looks like the last time you closed LrC, you either force quit it, or it crashed. As a result, the lock file is still in place. As a result LrC thinks a catalog is already open and will not by design open again.

Mind you, your error mentions a unistall, not a open, so not the same, but check.

see:

https://helpx.adobe.com/lightroom-classic/kb/lightroom-error-catalog-cannot-be-opened-lrcat-lock.html

Read carefully, and make sure you are deleting the correct file, not the catalog. Use caution.

If no lock file exists, then this is not the cause.

FYI for anyone else if you get the error "failed to initialize camera raw" my post above will fix that issue I had the same problem on MAC

I had a similar issue that I just fixed apparently it had something to do with other permissions on my MAC not letting the app open I had to go into the terminal and run a script that can be found on Adobes website.  or you can follow this YouTube video to show you how to do it. https://youtu.be/LPysUb1TNHk?si=RUj0cfoCGWTCd_jh 

I hope this fixes your issue it fixed mine and I was so happy when it finally worked!