It is hard to have pity for Lady Macbeth because she urged her husband to kill the king.  However, you could say that she showed remorse and that makes her worthy of our sympathy.  A person can do terrible things and still be worthy of pity.

First of all, Lady Macbeth did not kill Duncan herself, though she definitely encouraged her husband to do it.  When she got the letter saying that the witches had prophesied his being king, she was excited.  She really wanted that, and she got carried away. 

Lady Macbeth seems to want to draw on the harder parts of her personality to help her accomplish this.  If you interpret her this way, she is not such a bad person.  She just really wanted to help her husband succeed.  She had to draw herself up to it.

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 the access and passage to remorse,
That no compunctious visitings of nature
Shake my fell purpose, nor keep peace between
The effect and it! (Act 1, Scene 5)

She certainly doesn’t present a sympathetic figure when she emphasizes her manly features to encourage her husband, such as the comment about the baby where she would have “dash'd the brains out” (Act 1, Scene 7).  Her toughness aside, Lady Macbeth does a good job of planning the murder, but is unable to carry it out herself.  That is to her credit, at least.  She wasn't a murderer.

Also, Lady Macbeth may not be a great person, but she is not as bad as her husband!  She got herself in over her head, and for that you can pity her.  He kept killing after the first murder, which was not part of the plan.  She did not know what was going on, but she suspected something.  This is why she eventually went mad and killed herself.

Why do we feel both sympathy and repulsion for Lady Macbeth?

Ah, great question. Thinking about this lets us dig into the heart of the play.

We feel both emotions for Lady Macbeth because of the different strains the situation puts on her, and because of the way the different sides of her character come into play.

On the one hand, she is loyal to her husband, and wants him to be king. What could be better?

On the other hand, she drives him to kill when his conscience would weaken him.

On one hand, she knows her husband really well, recognizing that his character isn't harsh enough for the challenges this situation puts on him. She strengthens him.

On the other hand, again, she drives him to kill.

On one hand, she believes the information from the witches immediately.

On the other, she casts aside her own loyalty.

On the one hand, she clearly loves her husband, and is clearly wracked by guilt over what she's done... and on the other, she is so harsh that she says she'd kill a baby if need be, to get the job done.

I sympathize with her... but she also disgusts me.

Greg