I will begin with Frank Costello's life was saved by Lucky because Frank or Lucky was the one who convinced the other family heavyweights to invest heavily in Las Vegas and Bugsy's Flamingo fiasco.
Lucky told Frank to pay all them back from his own pocket or his life was on the line.

What are some other very close brushes with death?.....Too many of them.
Not dodging bullets type. The ones that got saved from sit-downs.