Yeah it's a little strange, my uneducated guessing leans towards something in Synaptic triggering it.
After install & reboot I clicked the update button/s from the welcome screen but realised after it started it'd fail as I hadn't run the chrome/update fix so cancelled the updates.
Ran the fix, then before trying to update again I opened Synaptic to change the Ubuntu Software's 'Download from' server to mirror.overthewire.com.au as it's a lot faster from my location than the default Server for United States, clicked Reload when prompted & that's when the fail messages I posted above happened.
Trying to update with the GUI then gave the same message as the google chrome error, 'couldn't fetch the package cache information lists'.
In the live USB I installed from it has 'beryl' in linuxlite.lists & linuxlite.lists.save, but both in the fresh install had 'trusty'.
Here's the steps if anyone's not sure and having the same issue:
Open Terminal & paste sudo leafpad /etc/apt/sources.list.d/linuxlite.list hit Enter, then enter your password, that'll open the correct file in a text editor, change the word trusty to beryl then go Ctrl+S or File > Save, close the file & Terminal.
Updates should then work.