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No, it could not. For the play to be considered a "tragedy" the tragic hero has to have some initial heroic qualities. We never see these in Lady Macbeth. She doesn't fall from a great moral height. She is ambitious, greedy and manipulative from the get-go.
Lady Macbeth's destruction is of her own engineering, and she has the same fatal flaw as her husband, that is, ambition. She however is not tempted by the evil spirits but calls upon them to support her in her sinful deeds. If we were looking for a tragedy with her name upon it, she would be required to have had another honourable pathway open to her and to have had clearly recognisable virtuous qualities before the dreadful deeds began. He story is not a tragedy, but a warning.