Here's how I've been looking for cached pages in Google. I suggest you copy this post if you're invested in collecting lyrics and suchlike, and maybe experiment to find what's works for you.

Find the latest mudcat page in archive.org (aka Wayback machine):
https://archive.org/
Enter mudcat.org
https://web.archive.org/web/*/mudcat.org

The circles mean there is an archive for that day.

Why are some of the dots on the calendar page different colors? We color the dots, and links, associated with individual web captures, or multiple web captures, for a given day. Blue means the web server result code the crawler got for the related capture was a 2nn (good); Green means the crawlers got a status code 3nn (redirect); Orange means the crawler got a status code 4nn (client error), and Red means the crawler saw a 5nn (server error). Most of the time you will probably want to select the blue dots or links. [FAQ]

Green circles are fine, too. Bigger circles means more stuff archived.

Find an archived mudcat page that shows the thread you want. Click it: if you're lucky you'll get the achived thread but often you'll get a load if gobbledegook that means it wasn't archived. You can go back and try an earlier archive, or you can look in Google's cache.

This is what I do; there are variations on this, using the '3 dots menu' - which depends on your device or computer, but this works for me on this tablet.

Copy the thread link - right-click, long-tap...

A thread link in archive.org looks like this: https://web.archive.org/web/20220401005550/https://mudcat.org/thread.cfm?threadid=171134&messages=4

The bit you want is at the end: https://mudcat.org/thread.cfm?threadid=171134&messages=4 (That's the original Chester FF thread.)
Open google.com in the browser.

NB You need to open Google's website. You (probably) can't put the 'cache:' keyword into your browser's URL bar. Some devices may redirect you to a Google app - I don't know if you can do the next bit with that - try it.

Anyway, I open this search page in the browser:
google.com

Type cache: and paste the copied thread link on the end. Then backspace over the part before 'https://mudcat.org' so it ends up like this:

cache:https://mudcat.org/thread.cfm?threadid=171134&messages=4

Hit enter, The result should be one of:
- A google page saying the archive doesn't exist
- The achived thread you hoped for
- An archive of a newer thread which has the same thread number - 1771134 in the example

As should be clear if you've read this thread, the sooner you do this after a crash or restore, the more likely you are to find the cached thread before it's overwritten.