Lucchese got a lot of press back in the 50s and they always spelled it "Luchese". You can see it spelled that way in old FBI documents too. I assume when they started to do more thorough research on these guys they realized it was spelled Lucchese. You can see it spelled that way in the Lucchese Family chart they had when Valachi testified.
This article has the man's signature in it and he has written "Lucchese"
https://www.newspapers.com/image/415687288/?terms=luchese&match=1From the Al D'Arco book:
"In a bid to avoid notoriety, the father juggled the spelling of the family name. Police and newspapers spelled it as "Luchese." Joe Valachi gave it an extra "c" when he began singing to prosecutors. His own preference was "Luckese." Jokesters had teased him with rhymes of "cheese," he explained. That's how the name was carved on his tombstone when he died in 1967."
