I can understand the previous suggestions about checking free memory, because Firefox has a reputation for maxing out RAM usage and slowing to a crawl, but since you are also seeing slowdowns in Chrome and Libre Office it's likely NOT a Firefox specific issue.
I suppose that you could have picked up some kind of browser related plugin malware, but if so, it should show up as either a plugin or extension under your Firefox "Add-ons", and you can easily see if Firefox is hogging system resources and slowing things down by simply rebooting and trying other applications BEFORE loading Firefox to see if they speed up when Firefox is not running.
From your description it sounds like ALL applications are lagging because they are getting bogged down by some MATE system related compatibility issue.
You can check if something is maxing out your CPU by opening the "Mate System Monitor" under your System Tools, and clicking on the "Resource" tab, which will show both Ram and CPU utilization, with the individual CPU loads for each core. If your CPU cores are maxing out, you can identify the culprit by opening a Mate Terminal and typing "top" without the quotes (type "q" and close the terminal to exit). If things are lagging and slow, but nothing seems to be overtly hogging 100% CPU, then it's almost always a kernel or low level driver issue.
If I had to guess, I would say that you are probably being hit by a pulse audio, bluetooth, or video driver related issue, related to UM18.04 compatibility on your specific hardware.
Here are some simple things you can try:
Disable Bluetooth (if you are using a bluetooth keyboard, try a USB keyboard instead)
Disable Pulse Audio
Don't worry, I'm not suggesting that you should accept that you will have to run MATE without these important features, just that you might want to disable them temporarily for troubleshooting.
Another thing to try is to open the "Mate Tweak" tool and change your window manager.
I have found that usually when there is a slowdown, it's related to a compatibility issue related to a driver update, or system library change, so the first thing to do is try to isolate which driver or library is causing the problem by trying to narrow things down a little. WiFi, Bluetooth, Pulse Audio, and Video Drivers are all good possibilities, because they all run at high priority, and can easily hang or slow the system if there are problems.