May be wrong there. Lewis claims that he and Sammy Davis, Jr. were very close friends and of course he and Dean Martin had been partners before their big split in the 1956 and yes Lewis knew Sinatra fairly well also.
And there is no doubt whatsoever that Sinatra was involved with the Mob. He thought it was cool to hang with the wiseguys but they thought of him as a Hollywood *sshole that they could use to get to Kennedy, which they did. The Mob used him to connect with Kennedy, and the Kennedys used him to get votes. He was a schmuck in my opinion who often treated people horribly.