The "Irish Session" as we know it today seems to have begun in postwar London; where it occurs to me that "session" has long been used as a general term for time spent drinking (the word originally meaning a period during which people sat, of course). A confluence, perhaps, of meanings in this case. I've mentioned in other discussions Hazel Fairburn's paper Changing Contexts for Traditional Dance Music in Ireland: The Rise of Group Performance Practice, which appeared in the Folk Music Journal (vol. 6 no. 5, 1994), and provides a useful summary and analysis. She doesn't discuss the use of the term, though she may have touched on it in the doctoral thesis on which the piece was based.