On the eve of the assassination there was a party at Clif Murchison's villa. A lot of prominent people were there including J Edgar Hoover and LBJ's mistress - Madeline Duncan Brown. LBJ told her privately "after tomorrow those damned Kennedys will never embarrass me again".
I don't believe LBJ planned it but I believe he was aware of the plot and logically, as future president, had to have given his approval to the plan. At the time the CIA was working closely with the mafia. JFK only won the 1960 election because the mafia had used underhand means to swing the election in JFK's favour. Once in office, the Kennedys began an intense campaign against organised crime (the mafia). the mafia saw this as a betrayal. Sam Giancana (head of the Chicago mob) was under intense surveillance from 'G men' and wanted the Kennedys off his back.
The CIA felt is had been betrayed by JFK over his failure to adequately support the bay of pigs invasion of Cuba and JFK made no secret of his plan to fragment or 'subdivide' the CIA. There lies the seeds of a plan to kill JFK.
The mafia could not do it all as they did not have the means to execute the cover up. The CIA probably did not do the actual dirty work (the shooting) to avoid being implicated and getting their hands dirty.
For many years LBJ had a hitman called Malcolm Wallace. Wallace had killed for LBJ as far back as 1951 and LBJ had used his influence to get Wallace out of jail with a suspended sentence.
A single fingerprint found on one of the boxes at the so called 'sniper's nest' at the book depository remained unidentified for a long time until it was compared against the known prints of Malcolm 'Mac' Wallace. A print examiner with 50 years experience positively identified it as being Malcolm wallace's.
LBJ's motives are that firstly he had an intense dislike of the Kennedys, he also knew that unless JFK was removed the likelyhood was that he would never be president. JFK planned to drop LBJ as vice president and it's possible that LBJ knew that. LBJ had a very shady past with implication in murder. he knew that once he was dropped as vice president there was a distict possibility of him being investigated for murder or conspiracy to murder.
LBJ certainly gave approval to the plan and thereby was involved in conspiracy to the murder.