What excuse does Lady Macbeth give for not killing Duncan herself in Shakespeare's Macbeth?
It is in Act II, Scene ii, that Lady Macbeth reveals why she could not kill Duncan herself. Just before Macbeth returns with his hands covered in blood, Lady Macbeth says:
Had he not resembledMy father as he slept, I had done ’t.
For Lady Macbeth, then, the resemblance between King Duncan and her father prevented her from committing the murder. This is significant because it suggests that, deep down, Lady Macbeth is not quite as ambitious as we first thought. Specifically, it shows that she values her family more than she values power. Even though she planned the murder and made the necessary preparations, it was the love of her father that stopped her from committing such a violent crime. In other words, Lady Macbeth might not be as callous as the reader first imagined.
Note the contrast here between Lady Macbeth and her husband: while she is distracted by the thought of her father, Macbeth does not have the same familial concerns and is able to commit the "deed."
The episode you are referring to happens in Act II, Scenes 1 and 2 of Shakespeare's Macbeth.
In Act II, Scene 1, Macbeth decides that he will kill Duncan. He hesitates a bit, giving his soliloquy about the knife and whether he really wants to go through with the murder, but when he hears the bell his wife rings he goes and kills Duncan.
Although Lady Macbeth wants Duncan dead (and although she provides the knife for Macbeth to use), she doesn't do it herself. The excuse she gives is that Duncan, when sleeping, looks too much like her father.
Lady Macbeth certainly has the opportunity to kill Duncan when she drugs the grooms' drinks and then looks into the king's room. She says, however, that she would have killed Duncan had he not resembled her father as he slept. Her courage wilts when she sees the sleeping king who reminds her of her own father, so she leaves the job of murdering Duncan to her husband, Macbeth.