I've made a few different lissajous diagrams now, but initially it took me a while to figure out what was going on. When I googled for explanations, they were all either too 'mathsy' for me, or they were links to a live-coding environment called lissajous by Kyle Stetz (awesome live-coding environment btw).
Lissajous diagrams are very straightforward. They are just a cartesian co-ordinate system like you used in middle school, with one signal assigned to the x axis and another (usually related) signal assigned to the y axis. Yes, that's it. Super easy. Lissajous diagrams are often used in DAW plugins to represent stereo spread. They're a very good way of visualising stereo spread as you can immediately see the difference between the two channels. I regularly work with mono signals, so I don't always have two channels to use. What I do is grab a delayed copy of the same signal, and use that. The visualisation is similar, but what you're seeing is related to the 'temporal flux' (which is a shitty name, but it captures the concept) of the mono sound.
I hope this helps someone else figure out what's going on, and saves them from the live-coding environment's excellent