He's noy lying through hsi teeth, Pataki did pass some harsh gun laws when he first came in, however, to date, they have not been enforced. Rudy came in, and started to crack down hard on crime, Pataki came in, and brought back the death penalty. Even though New York still to date has not executed anyone, the police have stated its become a brilliant tool to use as a threat in interrogations, allowing for better pleas, more information. Cases where they would have had to go to court in a trial for 15 year manslaughter cases, are now plead down to that. I don't think Rudy did it by himself, I will give credit to Tom Bratton, but to also Pataki. Under Cuomo and Dinkins crime just exploded, especially with Dinkin's anti-cop attitude.
Although the state gun laws changed somewhat over that time period, the gun laws in NYC did not change - they're still stricter than the rest of the state.