From an 2013 account ( Link ) by Michael L. Gillette, who helped conduct oral history interviews for the LBJ Presidential Library:
"After the swearing-in, Lady Bird Johnson placed the missal and the typed oath in her handbag and carried them to Washington. There she entrusted the items to Dorothy Territo, the White House staff assistant who collected material for a future presidential library."
"More than a decade later, in the course of my work at the LBJ Library, I learned that the elusive missal was discreetly hidden among the Library's holdings. I raised the matter with Harry Middleton, the Library's director, expressing the view that we should offer the book to the Kennedy Library or the Kennedy family. Why keep it if we could never exhibit it or even acknowledge possessing it? Harry concurred and contacted the John F. Kennedy Library. Dan Fenn, the JFK Library director, presumably after checking with the Kennedy family, responded that the LBJ Library should keep the missal. Since neither President Kennedy nor his family had ever used it, the volume had no sentimental value to them. Besides, its only historical significance related to President Johnson. The missal is presently on display at the LBJ Presidential Library."
From another site:
"It is believed the missal was a gift to the president from Father Albert Pereira, who administered to the small parish of St. Stephen the Martyr in Millersburg, Virginia, population 1,000, where JFK and his family spent their weekends away from Washington." ( Link )
Manchester's terming the missal a "bible" and Kennedy's most-cherished possession that JFK read all the time ( 
) reflects a "Northeast Liberal" bias and post-assassination reevaluation. It's less obvious in the Jim Bishop book. Poor LBJ couldn't catch a break from the Northeast Liberals (in the 60s, it was a concentration of political power and media--TV networks, Time-Life, publishers--that was literally located in the US Northeast).
That was public consumption. In Washington, LBJ benefited from long-serving Texans who were powerful in committees, as House/Senate Leaders, and as White House advisors.
Thanks again Jerry! That appears to be a reasonable solution to the mystery. And it accounts for both Manchester not having a more accurate account and that the missal was apparently offered back to the JFK family but they essentially said “keep it”.
Ladybird was a smart lady. And I imagine that, under any other imaginable circumstance, she would have asked Jackie, or someone else, if she could have the missal. Wow, this is an interesting aspect of the succession. I learned a lot.
