I have always gone straight to LSP after cutting and buffing with Menzerna but FWIW, there's a similar discussion going on in the current "Duragloss 501 and cutting/compounding" thread started by member Mike Honcho. I've never felt the need to use a "cleaner" after a 2 step correction before applying my LSP's but there are some who like and use that approach. As a result of that thread i AM going to try it on my next correction job to see what it yields from the extra effort. I do wipe down with Car Pro Eraser after my final polishing step but i think you are asking about a machine applied pre-LSP cleaner for a deeper clean of the paint.
To answer your question...no, i don't think you NEED to but would you benefit from it by doing it? Some think so and i'm certainly going to try it for myself. It certainly won't hurt anyway. Is it worth the extra time?