If you listened to the tapes of conversations between LBJ and J Edgar Hoover, it is pretty clear that LBJ had no involvement. He was wondering if he himself was among the targets that day.
LBJ did deliberately prevent a proper investigation into the assassination, however. If you listen to his conversation with Earl Warren, you can see that his priority was in preventing WW3. He believed that if the public believed there was a conspiracy, they might assume Castro was behind it and there might be pressure and escalation that could lead to nuclear war.
Warren's mission was to prove the lone gunman theory to the public's satisfaction.