Lansky and Luciano were chums since boyhood. Lansky, Luciano, Costello and Siegel were all proteges of Rothstein. But, during the Twenties, Luciano was associated with the Masseria family, while Lansky and Siegel did most of their work together.

During the Castellemmarese War of 1930-31, Salvatore Maranzano cajoled and then tortured Luciano into betraying Masseria. Lansky put together the squad (Siegel, Adonis, Anastasia) that murdered Masseria. Maranzano then appointed Luciano head of Masseria's family. But he was plotting to whack Luciano. Lansky then put together the hit squad that whacked Maranzano.

The producers of "Boardwalk Empire" are entitled to take many liberties with history to keep the story interesting. But, for the record, there's no evidence that Luciano, Lansky or Capone were ever in AC until a big gangster convention in 1929, or that Rothstein had any business with Nucky Johnson.