Discuss three factors which contribute to the downfall of Lady Macbeth.

There are more than three factors which contribute to Lady Macbeth's downfall but I will discuss three which, I believe, are the most pertinent:

1.   Lady Macbeth's avarice, which is an excessive greed for wealth and material gain. The Macbeths were already wealthy since they were titled landowners. Even though her husband had been generously bestowed another title, Thane of Cawdor, to add to his existing one, Thane of Glamis, it was not enough for Lady Macbeth. Their prosperity and stature had been doubled but she still wanted more. She sought the 'golden round' and wanted to be queen of Scotland.

Instead of being satisfied with her husband's new reward, she saw it as an opportunity to bring them closer to becoming king and queen of Scotland, as she states in Act 2, scene 5, after receiving the good news:

Glamis thou art, and Cawdor; and shalt be
What thou art promised:

The witches had promised her husband that he 'shall be king hereafter' but Lady Macbeth fears that he does not possess the ruthlessness to achieve that ambition by taking the shortest route, i.e. assassinating the king and probably his sons as well. She, however, is driven by ambition and wants to encourage him to execute Duncan. She wishes that he should rush home so that she can do so:

Hie thee hither,
That I may pour my spirits in thine ear;
And chastise with the valour of my tongue
All that impedes thee from the golden round,
Which fate and metaphysical aid doth seem
To have thee crown'd withal. 

It is Lady Macbeth's excessive greed that drives her to commit, with her husband, the most heinous of all crimes - the murder of her king. She carefully plots his assassination by getting Duncan's guards drunk and creating the perfect situation in which he can be killed. He would be asleep and, therefore, at his most vulnerable. It then becomes easy for Macbeth to kill him, unchallenged, without leaving any witnesses.

This malice is what later eats away at Lady Macbeth's conscience. She then cannot sleep and is tortured by images of blood on her hands. She slowly loses her sanity and seeks reprieve from her torment by eventually committing suicide.

2.   Lady Macbeth's relentlessly ruthless nature.

Added to the fact that she was overwhelmed by greed, lady Macbeth was also ruthless. She maliciously plotted her king's murder. She showed no remorse and found her husband's reticence to continue with their plot a weakness. She criticised him for being a coward and for making empty promises. She uses a shocking illustration to depict her determination when she tells Macbeth in Act 1, scene 7:

...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.

She uses this terrifying image to encourage her husband to be relentless. She also blackmails him into furthering their purpose by threatening that she would, henceforth, use his timidity as a measure of his love and commitment to her. When he expresses doubt about their malicious venture, she guarantees that they will not fail.

It is this relentless pursuit of her ambition that eventually awakens the monster in her husband. Once Macbeth has killed Duncan, his thirst for blood becomes an overwhelming factor in their lives. He becomes ever more merciless and cold-bloodedly executes whomever he deems a threat. His bloodlust spares no one. He has Banquo killed and wipes out Macduff's entire family.

Macbeth becomes so obsessed with killing that he starts neglecting his wife and his callous enterprise later becomes too much for her to bear which eventually drives her over the edge. She imagines terrible visions of death, blood and murder as she walks in her sleep. Her anguish is most pertinently displayed in Act 5, scene 1:

Out, damned spot! out, I say!--One: two: why,
then, 'tis time to do't.--Hell is murky!--Fie, my
lord, fie! a soldier, and afeard? What need we
fear who knows it, when none can call our power to
account?--Yet who would have thought the old man
to have had so much blood in him.

The thane of Fife had a wife: where is she now?--
What, will these hands ne'er be clean?--No more o'
that, my lord, no more o' that: you mar all with
this starting.

Wash your hands, put on your nightgown; look not so
pale.--I tell you yet again, Banquo's buried; he
cannot come out on's grave.

It is this deep despair which eventually drives her to her death. 

3.      The depth of Macbeth's brutality 

As already mentioned, Lady Macbeth's persistence awakens a malicious monster in her husband. Once he descends into the depths of evil, he becomes the epitome of a cruel, heartless tyrant. It is ironic that he believes the witches' lies about his invulnerability and his charmed existence, yet is still insecure and suspicious. He becomes paranoid and seeks to destroy everyone he deems a threat.

Macbeth's unrelenting malice and bloodlust become ruling elements of his and, therefore, also his wife's lives. He admits that he is so steeped in blood that there is no turning back. He says as much in Act 3, scene 4:

...I am in blood
Stepp'd in so far that, should I wade no more,
Returning were as tedious as go o'er:
Strange things I have in head, that will to hand;
Which must be acted ere they may be scann'd.

This suggests an even deeper descent into perfidy. Lady Macbeth realizes that her husband has become unstoppable and she is distraught by guilt and regret for having been a part of it all. Ultimately, she has no choice but to take her own life in order to relieve her from torment.