The term "Lissajous" when applied to object and or body movements refers to continuous circles/loops and patterns of loops that your body can make.
When you peddle a bike you are making lissajous ratios loops with your feet. Anything you do can be lissajous. "Lissajous-Do" which is what Lee teaches is a course in how to use your body's natural flow ratios to their full potential.
The word Lissajous all started when this guy in France with the last name "Lissajous" many many many years ago discovered that sound moves in patterns that resemble waves of motion. It wasn't until the 80s (I believe that's right) when Roy Williams, Lee's Teacher, discovered that the human body also moves in patterns of motion that resemble these "Lissajous waves". So in short, Lissajous-Do is the system for learning how to use your body's natural patterns of motion to their full potential. I hope this helps.
The first picture in the original post is a diagram on how to turn downwards figure eights with chucks into upwards figure eights without stopping the flow. You can notice how it resembles a figure eight, with an extra ring around it. The extra ring is called the commanding ring, it's the one that will take you out of your figure eights into other moves and back again without having the stop the chucks in motion.
