David Scull/The New York Times Mayor Rudolph W. Giuliani, left, at a 1995 news conference with Senator Charles E. Schumer, Democrat of New York, and James S. Brady, who was shot in the assassination attempt on President Ronald Reagan. As mayor of New York City, Rudolph W. Giuliani became the favorite Republican of gun control advocates. He spoke in favor of a licensing system for gun owners that would require trigger locks and firearms training, and he lobbied Congress to outlaw most military-style assault weapons. He was the only Republican mayor to join a lawsuit by dozens of cities...