Natalie is crazy. Certifiably. She's not afraid to kill, to take the lives of others. I mean, she has this trigger in bleach, she sees it as evil, and she needs to take out the evil in the world by killing those who use bleach...
And, Ernie was the one person in life who made it all ok, for her. He took care of her and watched out for her, and she felt like she could connect with him. She learned all her miniature work from him, from his teaching. She loved it, and found joy in their shared hobby.
He took his life to protect her, in hopes of sparing her, in hopes that it would all stop. She didn't get the message, though, and she felt suddenly very alone in the world. The one person who could make things ok was Ernie, and because of Grissom's actions (in her mind), he was gone. So, she sets about making him suffer, making him miserable.
You know the old cliche that misery loves company? She wants to take him down, to hurt him, to break him. Killing him is too easy. She wants him to suffer. So, she figures out that Sara is special to him, like Ernie was special to her. Her understanding of relationships is very limited, and all she knows is that Sara is that one person who can make things ok for Grissom. Since Grissom tore that person out of Natalie's life, in her mind, she has to tear his away. She has to go after Sara.
So, she takes Sara. She hurts Sara. She makes Grissom suffer. When she's in the room with him, he's already suffering, but she's still angry, still out for vengeance. The idea of leaving him bleeding to death, never knowing what happened to Sara is suddenly appealing, hence the fantasy of driving an exacto knife through his jugular. However, she has no exacto knife on her, so she sings. She blocks him out so she doesn't have to hear him because she has no intentions of helping him. She wants him to hurt, to ache, to know what it's like to have that one person who offered security and some sense of normalcy torn away.
I think that's why she asks if he loves Sara. She wants to make sure she made the right choice, to make sure that it hurts, that he's breaking, that he knows what it's like to be so terribly alone in the world. In her eyes, she's been doing the world a favor, taking out those who use bleach, who would do terrible things in the world. Ernie didn't use bleach, so Ernie was good in her eyes, and Grissom took away the good. That makes him evil, and in essence, bleach. So, she has to make bleach suffer, make bleach hurt.
This probably makes no sense, but I wanted to jump in and explain my thoughts before bed.