The fingerprints of Fidel Castro, the Cuban DGI, the KGB, and the New Orleans Mob are all over the case.
I personally believe that Fidel made the Mob Boys a better offer than the one they had from JFK. JFK was trying to kill Fidel with Mob hit men. Unfortunately, the CIA was penetrated at a very high level and Fidel knew everything. He struck back
LHO was a perfect instrument for Fidel. It is interesting that the KGB spent 10 years trying to convince the CIA that they had had NO interest in LHO while he was living in the USSR, this at a time when ANY visitor to the USSR had 24/7 KGB coverage and an assigned Intourist "Guide."
Cuber wouldn't be ruled by communists if the US government had finished Castro off years ago in an action designed to win.