In Macbeth, how does the news about King Duncan's expected arrivial affect Lady Macbeth?
It is clear that this important scene, incidentally the first where we meet Lady Macbeth, reveals a lot about her and her motivation for her actions in the play. The part you refer to comes just after she has received Macbeth's letter telling her about the witches' prophecy and where she gives a soliloquy revealing her fear that Macbeth will not be resolute enough to seize the opportunity to make these prophecies realities. When the messenger comes, informing her that King Duncan will stay at their place that very night, it is clear that she immediately determines to kill him, invoking the spirits to take away any kindness and make her cruel enough to engage in the act of regicide:
The raven himself is hoarse,
That croaks the fatal entrance of Duncan
Under my battlements. Come, you Spirits
That tend on mortal thoughts, unsex me here,
And fill me, from the crown to the toe, top-full
Of direst cruelty! make thick my blood,
Stop up th'access and passage to remorse;
That no compunctious visitings of nature
Shake my fell purpose, nor keep peace between
The'effect and it!
It is clear therefore that Lady Macbeth decides that King Duncan will not leave her home alive - now she just has to persuade Macbeth that this is the right thing to do.