Movie Trivia Game Show of Death

"Okay, very good. They all get to live...for now..."

"What do you mean, for now..." you say...

"On to the $8,000 question" says the voice, without answering. "If you answer correctly, you will be up to $8000 in winnings. And your grandmother on your father's side will get to live. If you answer wrong, we will slowly kill her with a butter knife."
You wonder. Your grandmother on your father's side was always pretty mean to you growing up. Maybe you should tank this question and let her die. But you'd also like to win that cool million. And you don't want the rest of your circle of family and friends to die just because she was a bitch.
"For $8000 and the lives of the people you care about, (not necessarily including your your paternal grandmother), who directed the Lord of the Rings trilogy?"