Robert Caro's Passage of Power appears to address your question the best. Caro wrote 4 books on LBJ that are generally chronological - his formative years, college campus politics, US House and Senate, then VP and Pres, so Passage is the one you want. Well, all of them are the one you want eventually.

To you question - badly. LBJ always had a kiss up, kick down aspect to how he dealt with people. When JFK was really too young when elected to public office at first bc Daddy's money and influence, then dressed like a spoiled rich college kid, then got a reputation for not being an especially hard worker, LBJ noticed.

When JFK (grudgingly) chose LBJ as his running mate, and during the following 3 years, LBJ always made the effort to be deferential to JFK's face. Things were more prickly with his brother Robert, but face to face interactions always showed careful, deliberate propriety.

Meanwhile both Kennedys kept LBJ out of the inner circle. When there was a funeral in some tropical country on another continent, they sent LBJ. This is always the VP's role to some extent, but more so this time. Kennedy's people accidentally on purpose kept not even inviting him to meetings that a VP reasonably may expect to be a part of, especially with LBJ's legislative resume.

Kennedy's closest friends/advisors were well to do, entitled, Ivy League Northeasterners. LBJ worked his way through the decidedly lower tier Southwest Texas State Teacher's College (now Texas State U, and better). They called LBJ "Uncle Rufus Cornpone" or similar behind his back but lots of times...so that LBJ found out over and over. The chip on LBJ's shoulder, or the others' shoulders was HUGE. Of course all the Ivy League types were entitled to write a book after they left the White House; they all shat upon LBJ.

Caro passed on a disturbing anecdote that illustrates the point (and the book has long since been returned to the library, so this is in soft focus now.) A few years into JFK's term in office, someone had returned from the Deep South with lots of film footage of Black and White poverty among sharecroppers and so-called hillbillies. All the big shots were watching this footage in that cinema room when someone remarked on a child "dressed in rags." LBJ lost it. He lost it so thoroughly that the anecdote appears to get mentioned by several people in their diaries or other memoirs (says Caro). LBJ who grew up between barely-middle-class and poor, and surrounded by poverty, shouted "THOSE ARE NOT RAGS! THOSE ARE PATCHED. CLOTHES." Imagine all 6 foot 4 of LBJ 2 inches from your face shouting that while veins are popping out of his much-redder-than-usual forehead and neck. It partly speaks to Caro being a good author, but that has stuck in my mind for 5ish years now. To live your formative years in such poor circumstances that this distinction would occur to you, then be surrounded by Ivy League trust fund babies, it's a big deal.