I know some of you mob historians can answer this question. Over the years, which LCN bosses from America have traveled to Italy to conduct business?

Good question Joe Bonanno ofcourse several times.

Carlo Gambino, Carmine Galante.

Joe Profaci, he played a major role in restoring the peace between the two warring Greco clans after 'Piddu the lieutenant' of the Giardini Greco family sought his advice.

Before Appalachian, all bosses went to Sicily or Italian every few years to meet with heads of the local families. Cleveland members, Joe Lonardo, Frank Milano, Al Polizzi, John Scalish, Detroit Members Salvatore Catalanotte, Bill Tocco, Joe Zerilli, Pittsburgh members Stefano Monastero, Frank Amato, and John LaRocca are some of the many. After Appalachian, the bosses cut back, but it was more of the he was born and grew up in Italy they meet with the other bosses from Sicily and Italy. Underbosses and Consiglieres, Capos, and soldiers also meet with their cousins, and usually served as an emissary so as not expose the connections, even using retired members and former administration members. After Appalachian, Bosses still meet with their cousins, examples include Joe Bonanno, Joe Profaci, Joe Zerilli, Stefano Magaddino, Joe Cerrito, John Scalish, John LaRocca, Carlo Gambino, but they lost alot of face with the Appalachian fiasco.

https://en.wikipedia.org/wiki/Grand_Hotel_et_des_Palmes_Mafia_meeting

Meeting for make a deal on the heroin traffick.


Among the American mafiosi present were Joe Bonanno, his underbosses and advisors Carmine Galante, John Bonventre and Frank Garofalo, as well as Lucky Luciano, Santo Sorge, John Di Bella, Vito Vitale and Gaspare Magaddino. While among the Sicilian side there were Salvatore "Little Bird" Greco and his cousin Salvatore Greco, also known as "l'ingegnere" or "Totò il lungo", Giuseppe Genco Russo, Vincenzo Rimi and Filippo Rimi, Angelo La Barbera, Gaetano Badalamenti, Totò Minore, Rosario Mancino, Calcedonio Di Pisa, Cesare Manzella, Gioacchino Pennino and Tommaso Buscetta.

To thwart eavesdropping FBI agents, Massino travelled to Mexico, France and Italy to discuss business with his lieutenants. The feds claim Massino took trips when he needed to take care of important business, like making Graziano acting consigliere.

Accardo travelled to Italy lots of times but I dont have any info if he met some of the local bosses, although we have info that he had contacts with deported mobsters like Dom Roberto. Also, Outfit "consigliere" Gus Alex once allegedly had a meeting in Rome with some "unknown" guys. During those days Alex was one of the Outfits prime messengers for Europe.