Lissajous curves are direct analogue displays of complex waveforms on two axis. They're transient and quite difficult to read until you start to equate the impact of maths on the waveform. At the most basic - bring in two versions of the same sound, and if they are identical then you get a straight line. If they are out of phase, things start to get interesting. Even more intriguing is where the two frequencies are harmonically related - the actual maths for the display is too much for my school maths but the shape produced by comparing say 1000Hz and 2000Hz is the same as comparing 5000Hz to 10000Hz - so the relationing between x2 x4 x8 etc can be seen. Feed in music, rather than tones and the display just fills up and goes crazy, with any diagnostic purpose very difficult to determine. Stereoscopes, usually software based nowadays produce a display that also has a straight line for mono, but a gradually expanding area as the two signals contain locational information. The ones built into DAWs give music results - they show how busy a soundstage is, they reveal phase issues and other faults. Lissajous figures have no processing - when I was a teen I took an old TV home, disconnected the scan coils and connected the 2 pairs of wires to my hifi - the speaker output deflected the beam that was, with no input, dead centre, and the amazing shapes and wildness of it were a never ending amazement! Connecting it to a synth was much better - especially when you added in the octaves and filters - I learned quite a lot about waveforms from my home made scope.
When you mention speakers going backwards, I assume you mean like a guitar cab with an open back? If you go behind, indeed the signal is inverted as back is front and front is back. Keep in mind that what we often call 'phase' is actually polarity. Phase is measure in degrees of 'lag', as in it is delayed. swapping wires around results in an inverted image on a scope - the phase is the same, but positive going or negative going - phase can be linked to multi channel stereo, but is really a time thing. Stereo imagining involves time of course, but often just amplitude.