Laurence R. Hunt says:
Mr. Richardson will be 93 on February 6, 2017. The fourth volume is at least two years behind schedule, but Mr. Richardson speaks of still working on it this year, in an interview with Alain Elkann. He states that he is "up to 1939," and that he hopes to "get through the war," either through 1940 or 1944. He reports that he is still working daily on the project with three assistants. I suspect that vol III may yet be the last complete volume, or hopefully, that Mr. Richardson's current notes can become the source material for a fourth or even final volume to be compiled by a successor, perhaps one of the three assistants he speaks of: http://alainelkanninterviews.com/john-ric
Read the article. It makes you feel like you want to read the biographer's life story - equally as interesting. John Richardson is still in New York (I've always wanted to meet him) and working on researching Picasso. I can only hope the fourth volume is on the horizon!