With the help of J. Edgar Hoover. Robert Kennedy as Attorney General did not bow to Hoover as others had and none of the Kennedys liked LBJ. They considered him a hick. Hoover was protecting the mafia, claiming there was no such organization, and RFK was going after them hard, probably to protect his families own interest in nefarious activity.
LBJ killed others before the Kennedys, starting with an Agriculture Department investigator looking for the phantom silos from which LBJ's friend and close associate, Billie Sol Estes, was collecting storage fees from the government. Exposing Estes would also expose LBJ. The inspector was shot in the back six times with a bolt action rifle that was left at the scene. The coroner's ruling was suicide. The coroner was a friend of LBJ.
After JFK they killed RFK because of his political threat to LBJ and continuing opposition to Hoover. The prize in LBJ's fevered mind, other than continued political power, was Jackie. You should listen to the creepy calls he placed to Jackie, wanting to be John Jr. and Caroline's daddy. She also thought LBJ was behind her husband's death but she only said so in her last interview.
Hoover had rid himself of a pesky adversary.