Ok, so in hind sight purging a package that was marked as a critical package was probably a terrible idea, but I was only following the instructions of people from this thread.
I couldn't get default-jre to install (it complained about broken packages), so after a bit of googling I came across the article above. I typed the command
sudo apt-get remove --purge tzdata and hit enter. Then it warned me tzdata was a critical package. I hesitated, obviously, and tried to find more information on the package but could find almost nothing. I assumed it was some non-essential part of Lubuntu but was marked as critical simply because it was a system program (also, my fears were mostly abated by the exceptionally casual nature with which the posters in that other thread instructed the OP to purge his tzdata).
So I typed the phrase and hit enter, and…. it started removing EVERYTHING. All the stuff I had set up, was being removed. Then, as I was doing it over VNC and the VNC died, I ran to the physical screen. It was quickly crashing because my keep-the-vnc-going scripts were layering onto of each other and exponentially increasing in number. So with the GUI completely unresponsive (I waited five minutes and nothing would happen except more scripts occasionally appeared), I hit the reset button on the PC.
It didn't boot into Lubuntu but memtest(x86) for some reason.
So this is where we are right now. I'm asking for help on fixing it, because ideally I don't want to reinstall, but since I began writing the question I've realised I should actually just be able to extract my scripts and some config files and reinstall Lubuntu, as it's just a NAS with very little software installed.
How would you suggest I proceed?