Lady Macbeth wants Duncan dead because of her own power-hungry ambitions. If Duncan is killed, and Macbeth is made king, then she will be made queen. Macbeth becoming king and her becoming queen might happen without Duncan's murder, too. The witches never tell Macbeth how he will become king. They just plant the idea in his head. Macbeth realizes that, which is why he has such a hard time fully embracing the idea of murdering Duncan. He waffles back and forth a few times and even tells Lady Macbeth that he won't do it. He is willing to wait to become king.
Lady Macbeth has no such patience or quandary over killing Duncan. She sees an immediate path to the throne, and she "encourages" her husband to take it. Her whole "unsex me" speech is not a rejection of her sex in a literal sense. She is trying to say that she needs to be more like a (stereotypical) man to do what needs to be done: strong, powerful, less emotional, etc. Macbeth tells her that he won't kill Duncan and she gives one of the most unloving speeches in history.
"When you durst do it, then you were a man;
And, to be more than what you were, you would
Be so much more the man. Nor time nor place
Did then adhere, and yet you would make both:
They have made themselves, and that their fitness now
Does unmake you. I have given suck, and know
How tender 'tis to love the babe that milks me:
I would, while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out, had I so sworn as you
Have done to this."
Lady Macbeth insults Macbeth's manhood, and then she talks about taking a nursing baby off her breast and dashing its brains out. That's cold! No, I don't think she wants to kill Duncan because she loves Macbeth. She knows Macbeth doesn't really want to kill Duncan. If she loved him, then she wouldn't have pushed him so hard. She wants Duncan dead because she wants the throne for her and Macbeth.