I wonder how "involved" the Genovese were. Casso didn't speak directly with Gigante IIRC, he took his marching orders from Corallo and Christy Tick at the time of the bombing.

Not to say they didn't want Gotti dead. They warned the Gambinos that someone would pay for Big Paul, and at least one hit attempt was picked up on wiretap and taken seriously enough for the FBI to warn Gotti.

Lino's death most likely was due to the Casso/Paradiso beef that led to the hit attempt on Casso.