Macbeth benefits from Lady Macbeth’s death because first, he now has no one to tell him what to do, and second, she will not tell anyone that he killed Duncan.
In Macbeth, Lady Macbeth benefits from Macbeth’s rise to fame. She encourages him to kill Duncan so he will be king.
But screw your courage to the sticking-place,
And we'll not fail. (Act 1, Scene 7, p. 24)
He gets a little tired of her telling him what to do. She comes up with the plan, she forces it on him, and she makes sure he executes it exactly. He starts to try to pull away from her. When she asks what he is planning after he is king, he refuses to tell her.
Be innocent of the knowledge, dearest chuck,(50)
Till thou applaud the deed. (Act 3, Scene 2, p. 46)
So Macbeth benefits from Lady Macbeth’s death in that she is no longer around to tell him what to do and nag him.
The second way in which Macbeth benefits from his wife’s death is that she is not around to tell anyone that he killed Duncan. As his accomplice, Lady Macbeth knows everything. Toward the end of her life, she is beginning to succumb to guilt. She starts to lose her mind.
Out, damned spot! Out, I say! One–two—
why then ’tis time to do't. Hell is murky. Fie, my lord, fie! (Act 5, Scene 1, p. 77)
She certainly babbles too. At one point she talks about “the old man” and how much blood he had in him. Clearly, people listening don’t have to try hard to put two and two together. As long as Lady Macbeth is alive, she is a threat to him.