Totally agree with these two posts. Costello had lost all support when Genovese took over. Lucchese being a wheeler and dealer is hugely underated by most of us. Evidence support Lucchese being behind and in the shadows of many things that occured in the late 1950s/early 1960s. He desired Costello´s power, position and influence with the NY politicians and judges. He used a number of people to get what he wanted; Genovese, Gambino and Magaddino all did his bidding in one form or another. And as TB stated, Lucchese´s conniving may have started during a Commission meeting where he was accused of wanting Costello dead.
Agree on Lucchese being underrated. Just one correction, at a Commission meeting, Costello uncovered a plot by Lucchese to kill Anastasia, not himself.
On Costello, a comparison might be made with Paul Castellano. Both men had a reputation for being more white collar. As underboss, Vito rallied support with blue collar faction.