With all due respect, thats not possible Hollander. In fact, it's patently impossible.
Because they were very close, Lansky may have passed some messages to several key capos from Luciano. He may have even executed some of Luciano's orders and requests.
But, as a non-Italian and a non-member associate, no way, no how, was he "leading" the Family, (as their "acting boss" no less.)
That would have been a direct slap in the face to every goodfella in the family, and by extension, to all other goodfellas. Understand?
He was Luciano's eyes and ears in the US. After the departure of Genovese Lucky probably appointed Costello as acting boss. However when Vito and Frank were at odds the role of Lansky became more important.