Lady Macbeth is driven by ambition and a desire for power, she is a stronger personality than her husband, Macbeth. She is consumed with the idea of becoming queen, once she discovers the witches prophecy and discusses with her husband the plot to murder Duncan when he comes to their home that evening for a visit, she is crazed when Macbeth tells her that he has decided not to kill the king. She accuses him of being disloyal, unfaithful to his promise to her.
"Lady M. What beast was't, then,
That made you break this enterprise to me?
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
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." (Shakespeare)
In this speech, she tells her husband that if she had made a promise to kill her own child, she would rip the child from her breast, while it smiled at her, she would kill it, if she had promised Macbeth that she would do it.
The relationship that the Macbeths have borders on odd obsession, the type of love that requires extreme commitments to declare love, to prove love. Lady Macbeth is driven by both personal ambition and by the need to have her husband complete the task that will elevate him to the throne.
Even though she wants to be queen, I believe that a big part of the reason that Macbeth goes ahead with the murder is to prove to his wife that he loves her. In this regard, I feel that Lady Macbeth demands this proof from her husband, she requires him to commit this act of murder to prove his fidelity and love for her.
What is really tragic and interesting if you analyze the question in this way is that once the Macbeths become the King and Queen of Scotland, their relationship becomes fractured and they lose their connection with each other.
"But the union between Lady Macbeth and her husband has disintegrated under the weight of the evil that they have done and of the further evil that Macbeth does for their sake."
By the time Lady Macbeth throws herself off of a building, committing suicide, you would expect that, based on the deadly love that they shared, that Macbeth would fling himself off the same rooftop to follow his love into death, but he doesn't.