No. The police told her to be on the lookout for him, and he'd probably be coming after her. He was a serial killer on the run, he killed someone just to get into Lana's house. Lana is well acclaimed and the nations best journalist (she literally went back into her worst nightmare to expose Briarcliff). All she has to do is mutter the word "self-defense" and she's off the hook. Idk if it all made sense, but point is Lana won't be in prison for taking down a wanted serial killer.
EDIT: and in real cases the parents of the person killed can say it was "foul-play", but good thing is his father was murdered decades ago and his mother is Mrs. Banana herself so i'm sure no one will blink an eye over it