I'm interested in hearing what exactly you mean by "lay psychoanalysis." Analysis performed by someone who isn't a mental health professional? Analysis performed by anyone who never received formal analytic training?
It's an interesting question, whether there is such a thing. On one hand, Freud himself was a lay analyst. On the other hand, there's probably a reasonably large contingent of (orthodox) analysts who would assert that it can't exist for structural reasons (the setting, the lack of payment, the nature of the relationship, etc.).
Who dismisses lay analysts in this sense? Not even analysts do anymore (as evidenced by the acceptance of psychologists into analytic programs). You said not involving a "professional." Freud was talking about physicians.
I just meant that, if you want some kind of psychoanalysis, you don't necessarily need to go the professional route. Medically trained psychoanalysts don't really have a clear advantage over lay analysts in terms of insight.
It's an interesting question, whether there is such a thing. On one hand, Freud himself was a lay analyst. On the other hand, there's probably a reasonably large contingent of (orthodox) analysts who would assert that it can't exist for structural reasons (the setting, the lack of payment, the nature of the relationship, etc.).