What I should have said is that I don't think Lansky had any stock in casinos which weren't also partly shared by the Genovese crime family. Now this would be a problem if Anastasia was trying to muscle in on them but in my opinion, the more plausible scenario is that Anastasia wanted to have his own casinos in Havana and Genovese was not willing to share the wealth. Gambino readily assented to the plot because he then take over the family.

Edit: Just double-checked some sources and this is indeed close to what actually happened. Whether or not he was assassinated specifically for this, I do not know.