The mafia wasn't supposed to terrorize civilians. That brings unwanted attention from the authorities. In the old days, the authorities may be willing to not get too involved with mafia skirmishes between each other, but when it came to private citizens there would be more public pressure to intervene.

So Lefty would be in dilemma. He brings heat by whacking a private citizen and if he goes to jail he adds to his record which means he's a greater liability to get a long sentence if he gets pinched in a legitimate LCN racket. Best to pay the guy off