===========================
Install Updates could not fetch the package cache information lists.
Go to https://www.linuxliteos.com/forums/ and paste the log below into a new or existing thread for assistance.

============ Log ===========

Hit:1 http://repo.linuxliteos.com/linuxlite citrine InRelease
Hit:2 http://us.archive.ubuntu.com/ubuntu xenial InRelease
Hit:3 http://ppa.launchpad.net/nemh/systemback/ubuntu xenial InRelease
Hit:4 http://archive.canonical.com xenial InRelease
Get:5 http://us.archive.ubuntu.com/ubuntu xenial-security InRelease [102 kB]
Hit:6 http://ppa.launchpad.net/otto-kesselgulasch/gimp/ubuntu xenial InRelease
Hit:7 http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu xenial InRelease
Get:8 http://us.archive.ubuntu.com/ubuntu xenial-updates InRelease [102 kB]
Get:9 http://us.archive.ubuntu.com/ubuntu xenial-proposed InRelease [253 kB]
Get:10 http://us.archive.ubuntu.com/ubuntu xenial-backports InRelease [102 kB]
Hit:11 https://deb.opera.com/opera-stable stable InRelease
Get:12 http://us.archive.ubuntu.com/ubuntu xenial-updates/main i386 Packages [536 kB]
Err:12 http://us.archive.ubuntu.com/ubuntu xenial-updates/main i386 Packages
Hash Sum mismatch
Get:13 http://us.archive.ubuntu.com/ubuntu xenial-updates/main Translation-en [224 kB]
Get:14 http://us.archive.ubuntu.com/ubuntu xenial-updates/restricted i386 Packages [7,772 B]
Get:15 http://us.archive.ubuntu.com/ubuntu xenial-updates/restricted Translation-en [2,548 B]
Get:16 http://us.archive.ubuntu.com/ubuntu xenial-updates/universe i386 Packages [461 kB]
Get:17 http://us.archive.ubuntu.com/ubuntu xenial-updates/universe Translation-en [188 kB]
Get:18 http://us.archive.ubuntu.com/ubuntu xenial-updates/multiverse i386 Packages [7,996 B]
Get:19 http://us.archive.ubuntu.com/ubuntu xenial-updates/multiverse Translation-en [4,460 B]
Fetched 1,095 kB in 7s (154 kB/s)
Reading package lists...
E: Failed to fetch http://us.archive.ubuntu.com/ubuntu/...8172fd2faba5cb Hash Sum mismatch
E: Some index files failed to download. They have been ignored, or old ones used instead.

I would just try the install in a few hours. The errors are usually due to the mirror site the installer is using being updated. Or, you can choose a different mirror for the install, but you might have to do a manual install to have that option.

did you do that also?

Not sure what is at fault. As above stated a few.

This issue has been out there for years so many solutions exist.

Did you do this? Go to https://www.linuxliteos.com/forums/ ?