One of the reasons Lansky lived to age 81, and died peacefully, was that he was always willing to share--and that included Cuba. He was very tight with Cuban dictator Fungencio Batista, but he used his influence to allow other mobsters (notably Santos Trafficante) to have interests in casinos other than the Nacional, where Lansky's brother Jake reigned supreme.

In 1957, Hilton announced its intention to build a hotel/casino in Havana. The Cuban hotel workers' union wanted a big share in that hotel, and Batista appointed a Cuban, Roberto "Chiri" Mendoza, to be the local contractor. Albert Anastasia had been talking to Mendoza about getting a piece of the action. Mendoza had been staying at NYC's Warwick Hotel--as had Santos Trafficante--and Anastasia was seen in the hotel on the day he was whacked.

There's not much reason to doubt that Vito Genovese and Carlo Gambino arranged Anastasia's assassination. But, if Cuba was involved, the finger points at Trafficante, not Lansky.