There would be no reason to try to kill Frank if Lucky was still the head of the Family.

A man without friends is a man without power.
Lucky was friendly with a lot of powerful people, in his family and outside of his family. I guess it also depends on how Vito's faction felt about Lucky. From what I read Lucky was about making money for himself and the people that work with him. I don't know what reason anyone would have to back Vito over Luciano.

Btw a lot of the things I said about Lucky can apply to Joe, as far as relationships with people.