Remember that one of the thematic topics Macbeth centers on is this notion of ambition and how ambition can unravel a life and lead to destruction and downfall. This question is similar to asking how the three "weird sisters" are responsible for Macbeth's own death. They have introduced an idea of becoming king that sets him on a treacherous journey, committing violent act after violent act and sets his fate. Macbeth does this to (or for) Lady Macbeth. He writes her a letter, introduces the idea the witches have cast before him, forces her to think about becoming queen. And her own ambition takes hold.
Lady Macbeth is strong, at first, even more adamant and brave and treacherous than her husband. She doesn't think he can even commit an act of treachery: "Yet do I fear thy nature; / It is too full o'th' milk of human kindness / To catch the nearest way" (I.5.17-18). She knows he can't do it, and will have to push him, questioning his manhood and supporting him as much as she can.
Her support turns to physical action versus simply verbal support, as well. This is another argument for Macbeth's responsibility for her death. Macbeth botches the murders in Act 2, failing to leave the daggers behind that would frame the King's chamberlains. And it is Lady Macbeth who must return to the scene of the crime to replace the weapons. There she sees how much blood has been spilled; she sees the King and can't help but connect his appearance to her own father. She is now a full accomplice, rather than just being behind the scenes, and those images are burned in her mind.
All this leads to her inability to forget the deeds, the unnatural chaos she and her husband have set in motion, the guilt which will forever live with her. This pushes her over the edge. Macbeth's kingdom will be attacked, the tyrant King and Queen's reign will come to a bloody end (Macbeth's head is displayed), she cannot live with the guilt of their ambition, an idea she gets from her husband.