I will be writing more on Black Moon Lilith shortly Haizea. The origins of my research started after reading a psychotherapy paper on the treatment of character. It seems that someone else (a non astrologer) back in the 60's identified the "demon" part in ones personality. Its the part that sabotages things and throws things into chaos (ususally in therapy). The Demon and Lilith have their similarities however Lilith is more descriptive and encompasses ones potential creativity and other factors rather than focussing on pathology.
The transference/counter Transference model is a good one. Although these concepts do not rely on Lilith, a prominent Lilith can emphasise the factor. My moon lilith has been quite strong over the years, however more recently and with my evolvement as a psychotherapist - I find that Lilith can be very useful in my work with clients especially the ones I engage in relational therapy with. Here, the therapist works "in" the transference rather than viewing that from a detatched position and taking notes etc.
best
Kingsley