Lady Macbeth, according to Frye's Archetypal Chart, is not a tragic hero. Instead, she is a Supplient, one who provides vision of unmitigated suffering and helplessness. Like Jocasta (in Oedipus), Ophelia (in Hamlet), and Cordelia (in King Lear), Lady Macbeth suffers along the tragic hero. Macbeth's actions affect her more than the reverse. Her death presages his.
Clearly, Macbeth is the tragic hero of the play. It is ultimately his decision to kill Duncan. Yes, Lady Macbeth supports his plan, but he was well on his way to doing it, I think, with or without her help. Not only that, but Lady Macbeth cannot kill Duncan; she says he looks too much like her father. So, clearly she is an accomplice only.
Later, there will be a division of labor between the couple. Macbeth will continue to kill without Lady Macbeth's council. She disappears through much of Acts II and III and only has one memorable scene in Act V. Her death is not shown on stage, and it has little affect on Macbeth in terms of plot. Yes, her death elicits the "tomorrow" soliloquy, but Macbeth does not change course because of her death: he is resigned to it.
Overall, Lady Macbeth is a symbol of suffering, madness, and femininity who juxtaposes--but does not equal or surpass--Macbeth's tragic qualities. Though she is instrumental in Acts I and II, she is off-stage too much in Acts III-V to be a tragic hero herself.
'Macbeth' is a tragedy with double catastrophe: the death of Macbeth in the hand of Macduff preceded by the suicidal death of Lady Macbeth. In my view, Lady Macbeth's tragedy consists in her volitional self-sacrifice for the sake of her husband's 'vaulting ambition' triggered off by the 'supernatural soliciting'.
Macbeth's letter to Lady Macbeth intensifies in her a sense of involvement & participation so that her husband's desire for the throne is fulfilled. She invokes the forces of darkness to equip her with dire cruelty so that she can prevent 'the compunctious visitings of nature' and work out the horrid deed of murdering Duncan in their castle.
Lady Macbeth is tragic in the sense that she chooses to go against her basic womanly nature for her loyalty and devotion to Macbeth. But she is by no chance a 'virago'; she is not the 'Clytemnestra of English tragedy'. She undergoes fear and despair ever after the killing of Duncan; Macbeth independently plans to kill Banquo and his son, Maduff's family, and unleashes bloody terror in Scotland; Lady Macbeth feels more and more estranged from her husband's company, fails to come to her husband's rescue in the Banquet; suffers from mental degeneration leading to pathetic sleep-walking, her guilt and remorse avenging upon her mind to force a split; she dies a disconsolate death leaving her husband alone and exposed to defeat and death.
The way Lady Macbeth suffers deep within herself, her volitional act of standing by her husband backfiring to push her to the point of madness and death, I would like to consider her charater as sufficiently tragic, her death arousing in us a sense of waste which is central to tragedy.