It doesn't pay to get too literal about history in "Boardwalk Empire," but for the record:

Gerardo Machado attempted to steer Cuba toward an independent-of-Uncle Sam position in the early Thirties. He was deposed in a US-sponsored coup.

Meyer Lansky's interest in Cuba was in gambling, not booze. He did get into a booze-related business with his father in law after Repeal, but it failed.

As for not talking to Lucky too often: Lansky arranged the assassination of Masseria at Lucky's behest. Maybe that line showed him trying not to be associated too closely with Lucky, and thus be identified with the crime. Notice that Lucky acquired a droopy eye: That was inflicted by Maranzano's thugs after Lucky initially resisted betraying Masseria.

I don't know if that hand-cutting ceremony happened in real life, but Maranzano rewarded Lucky by putting him in charge of Masseria's family. In fact, Maranzano appointed the heads of all the five families at that Bronx meeting. But he made a fatal mistake: he declared himself capo di tutti capi at that meeting and demanded a monthly tribute from all the Mafiosi present. That didn't go over too well. Luciano reached for Lansky again. Lansky arranged for Maranzano's assassination in his office. Coincidentally: while Lanksy's killers were shooting and stabbing Maranzano to death, a hired assassin, Vincent (Mad Dog) Coll, was on his way to Maranzano's office to receive his final instructions for assassinating Luciano. The close timing is one of the reasons he was known as "Lucky."