Updating Firefox 87 to 110?

[Moltke]

It would appear I have Linux Lite 5.4, which I run as LiveCD. Is it possible to update the Firefox to version 110?

I think you can run a new version, but since you're running live, unless using persistence, updating it's not possible since all changes will be lost on reboot. But, you can:
1. Download new version from here https://www.mozilla.org/en-US/firefox/new/
2. Extract the .tar file.
3. Navigate to the extracted folder and launch Firefox.

Then you can save the ~/.mozilla and firefox (the one containing the files extracted from the tar) folders  to a flash drive or something, so next time you just have to copy those to the live OS and use it again.