This photo I found in the Getty Images collection answers a lot of questions about the President’s Private Dining Room. With the doors open, you can see a steward in what must be the little butler’s pantry. The pantry inside the dining room is in place in 1970, where it looks to be home to a movable TV cart (perhaps LBJ used the room as a dining room—Nixon seems to have inherited a round table in that 1970 photo).
It’s clear also from the new photo that there is no door on the north wall of the corridor to the Oval Office, so that whole space must be the president’s lavatory, and must have been so since the Reagan era. However, there used to be doors on that wall in the Nixon era and as early as 1962 but not in 1961 so that must have been to an earlier little pantry and a smaller lavatory changed by Kennedy late ’61/early ’62
I also just realized that the president’s lavatory used to be the narrow room later expanded to be the President’s Private Study. It’s clearly marked that way on the 1934 Time – Life floor plan. Now the President’s Private Study has changed too, for some reason. In the later Kennedy era, the door was was next to the Oval Office. But at some point, by the Johnson era it was moved to be next to the dining room and still is.
UPDATE: Reader Gary points out that the 1961 photo is flopped. Damn these photo editors! Don’t they know to put the shiny side up?