Luciano and his cohorts pulled off one of the great con jobs on Uncle Sam:

Soon after the US entered WWII, the government seized the French ocean liner Normandy, which was on a West Side Manhattan pier, and began to renovate it as a troop-carrier. A worker got careless with a torch, igniting some burlap sacks and setting a fire that caused the ship to capsize. The US Navy commander of the port suspected "sabotage" by "Axis agents" mingling with Italian and German longshoremen. Joseph (Socks) Lanza, Mob boss of the waterfront, took that info to Meyer Lansky. He brought it to Luciano in his upstate NY prison. Result: Lansky approached Judge Murray Gurfein, who'd been one of Dewey's prosecutors in the case against Luciano, with a promise: Lucky would assure that no further "sabotage" would occur on the docks, in return for better treatment. Lucky was moved to a "more comfortable" prison closer to NYC, and was deported in '46.

And, you're right, Lucky didn't help the Allies with the Sicilian landings because he'd been long gone from that island. Sicilian Mafiosi had been driven underground by Mussolini, who regarded them as a rival power. As soon as the Allies landed, the Mafiosi identified themselves as "Resistance fighters," and the allies bought it--restoring the gabellotti to their former positions and appointed them mayors, judges, etc. They got help from Genovese, who, ironically, had ingratiated himself with Mussolini earlier but moved to Sicily after the invasion to be "helpful" as a translater and go-between for the Allies and the Mafia. He bribed countless American officers to get access to scarce consumer goods, auto parts, etc., and shipped them to Naples where he ran the largest black-market operation in Italy.