ESR= Equivalent series resistance. In my eyes, thee only real way to test the integrity of a cap.
Using lissajous figures is like using a megger in a PM program. They can show you forms of any circuit with different draws, but you'd have to know what you were looking at prior to performing the test. Now, on thee other hand, if you had a KGU to compare the unit against, lissajous figures are priceless. Lissajous figures are useless to a service guy walking in blind, but as far as plant maintenance, and a good PM program, show me a meter with the two features combined, and send me an invoice.
Not too many people utilize ESR meters, or even have any need for a tester capable of lissajous readouts. BUTTTTTTT,...... if you know how to use them properly, they are worth every dollar

Fluke use to have the 867B, it had the "Component Test" function. That's what that function served, was graphing lissajous figures. They did away with it. Too bad, I say. I ended making my own in a 4x6" box to hook to my scope. Well worth it for $50.
As some have no idea of what exactly a "megger" shows, much, much less have any idea of lissajous figures and how useful they can be.