I recently installed phpList in a folder of my current joomla install (on share server in bluehost). I had to manually install it, and I can access the admin page.
Joomla is installed at the root folder (html_public) and phpList in a folder within it (html_public/phpList).
As said, I can successfully access the admin page of phpList (www.my-site.com/phpList/lists/admin) and configure it.
The problem is: every time I click on "save" to save an updated configuration, then it re-directs me to a 404 - not found throw by joomla (as it redirects to http://www.my-site.com/lists/admin/?page=configure#item_confirmationmessage). My updated configuration is correctly saved, and I can easily go back to it pressing the "back" button in the browser. I notice that phpList is not redirecting to the correct folder html_public/phpList/lists but to an incorrect one: html_public/lists.
I think there has to be some tweak to do in joomla and/or phpList to correctly define the folder it should direct the confirmation message.
I'm fully aware of the alternative of installing phpList to a subdomain's root folder, but at this point I'd prefer (if possible) to fix what I actually have.
This is what I ended doing, if it's of help to people looking for solutions.
It seems phpList is somewhat picky about the folder it's installed to.
In order to avoid conflicts with the already existing Joomla install, I had to create a subdomain and then make a clean re-install of it to a folder called lists within that subdomain. Any other solution (for example installing it to lists within html_public of my main domain) didn't work well, producing errors similar to the one described in the question. So, step by step:
lists within that subdomain's html_public folder. Make sure you follow the guide in phpList documentation