‘em. Had he not resembled
My father as he slept, I had done't.

The long answer, however, is that she did not kill the King because the play's author did not want her to kill him. Shakespeare wanted Macbeth to do the killing because the play is about Macbeth, what he does to become king and how this affects him afterward. Lady Macbeth exists as a character to give Macbeth someone to talk to. Characters in plays have to talk to each other in order to communicate information to the audience. Macbeth has no one else with whom he could discuss his most secret thoughts and feelings. His wife also serves to encourage him to go ahead with his ambition to become king by murdering Duncan. 

Then why does Lady Macbeth say that she would have killed Duncan herself if she hadn't thought he resembled her father? Mainly because Shakespeare wanted to explain to the audience why such a vicious woman didn't actually commit the murder when she had the opportunity. Shakespeare also wanted to explain to the audience that she "laid their daggers ready." Why was this necessary? Shakespeare probably wanted to explain how Macbeth was going to be able to get inside the King's bedchamber and assassinate him when he was being guarded by two men. Lady Macbeth's soliloquy informs the audience that she was an important accessory. She provided the grooms with drugged "possets."  (The word "possets" is glossed in one edition as "hot drinks, containing milk and liquor.") Her statement that she "laid their daggers ready" is intended to inform the audience that Macbeth will have the weapons available when he enters the bedchamber and, more importantly, that he plans to kill Duncan with the grooms' daggers in order to be able to frame both of them for the King's murder.

Why would these two men want to murder the King? They were "suborned." Someone who wanted the King dead had supposedly bribed the grooms to commit the murder.

MACDUFF:

They were suborn'd:
Malcolm and Donalbain, the King's two sons,
Are stol'n away and fled, which puts upon them
Suspicion of the deed.

When Macbeth returns to his bedchamber still holding the bloody daggers, the audience will understand that these daggers belong to the two grooms and hence will understand the whole plan: Drug the grooms, kill the King in his bed, leave the bloody daggers with the grooms to frame them and cast suspicion on some unknown person or persons who had a motive for wanting the King dead. Suspicion naturally falls on Malcolm and Donalbain after they flee, but the real mastermind might have remained a mystery otherwise. Shakespeare, who is responsible for everything that happens, has the boys flee because that makes it much easier for Macbeth to get elected as the new king instead of Malcolm, the heir apparent.

In Act 2 of Macbeth, Lady Macbeth and Macbeth act on their conspiracy to kill King Duncan, trying to force the prophecy to be true. In Act 1, we learn from Lady Macbeth that she does not think Macbeth has enough ambition to act on the plot. We also know that Macbeth is having second thoughts about killing Duncan, because of the new title Duncan has given Macbeth. It is curious, then, that Lady Macbeth doesn't kill Duncan herself. The answer is in Act 2, scene 2. While waiting for Macbeth to come out of Duncan's chamber, Lady Macbeth states, "Had he not resembled My father as he slept, I had done 't." Lady Macbeth sees a resemblance between Duncan and her father, which causes her to hesitate in killing Duncan. This fact adds another layer to Lady Macbeth's character, as it is the first hint at emotion she shows.

Lady Macbeth starts out as a strong female character (albeit with villainous motives) not commonly seen in Shakespeare. She has a sense of purpose and will seemingly stop at nothing to ensure her husband is on the throne.

Yet when it is time to commit the actual murder, Lady Macbeth stands solidly to the side, using this excuse:

Had he not resembled
My father as he slept, I had done't. (2.2.15–6)

Shakespeare likely needed a good excuse here to move Lady Macbeth back to the sidelines and allow her husband to commit the actual murder. First, she is fairly isolated, especially as a woman. Whom would she look to for support if she had committed murder? She has been the main source of strength in this power couple, so it is unlikely that Macbeth could have been an emotional or mental support if she became a murderess. There are no other women around her to fulfill this role.

Second, the historical context pointed to Macbeth needing to be the actual murderer. An audience could understand a man showing dominance, cunning, and leadership—taking what he thinks he deserves. But could they understand this plot if Lady Macbeth had committed the murder? It is likely that a strong, independent, murderous woman would have received an entirely different reaction.

Furthermore, where would this action then leave her throne-seeking husband if he had not had the fortitude to follow through with the plan and simply stood behind his wife instead? Also worth noting is that Macbeth was written early in the reign of King James I, further supporting the need for a strong male character, as Shakespeare and King James had a strong relationship.

Shakespeare needed to shift the focus from Lady Macbeth to the title character here, and these lines provide a convenient excuse for Lady Macbeth to slide into the background and for her husband to emerge as the man of action.

The answer to this question is given in act 2, scene 1, of Macbeth when Lady Macbeth says the following:

Had he not resembled
My father as he slept, I had done’t

In other words, Lady Macbeth claims that she would have killed Duncan had he not looked so much like her father while he slept. Lady Macbeth is alone when she says this, so there is no reason to assume that she is lying.

The interesting thing about this explanation is that it humanizes Lady Macbeth in a manner that we have not seen up to this point in the play. Although Lady Macbeth has previously seemed to be purely diabolical, here we see that she has emotional depth.

Of course, she still wants Duncan to be killed, and so she cannot be absolved altogether. Nonetheless, this is a crucial moment in the development of one of Shakespeare's most complex characters.

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 resembled

My 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."

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.

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.

I laid their daggers ready;He could not miss 'em. Had he not resembledMy father as he slept, I had done't.

While Lady Macbeth wants King Duncan dead, she feels more comfortable urging her husband to commit the murder instead of carrying out the crime herself. Lady Macbeth masterminds the assassination, convinces her husband to kill the king, participates in the crime by placing the daggers in Duncan's chamber, and spikes the servants' drinks. In act 2, scene 2, Lady Macbeth patiently waits for her husband to kill King Duncan and gives insight into why she does not kill the king herself. Lady Macbeth says,

I laid their daggers ready; He could not miss 'em. Had he not resembled My father as he slept, I had done ’t (Shakespeare, 2.2.11-14).

Essentially, Lady Macbeth says that she could not kill King Duncan, because he reminds her of her father. Her comment implies that she is not strong or violent enough to carry out the murder, which corresponds to the social conventions of Shakespeare's time. As a man, Macbeth must carry out the brutal act because it is part of his violent, masculine nature. Later on, Lady Macbeth cannot overcome her feelings of guilt and gradually loses her mind before committing suicide.

There are a few reasons why Lady Macbeth does not kill King Duncan herself.  First, in Act 2, Lady Macbeth says that the king resembles her own father, so therefore she cannot kill him.  More importantly, however, Lady Macbeth as a woman must follow the social conventions of her time.  Earlier in the play, she prays to the spirits and asks that they "unsex" her so that she might have enough cruelty to help Macbeth go through with the murder.  As a woman, she is supposed to be innocent and good-natured, so obviously committing murder does not fall into this persona.  When Duncan is found dead by Macduff, Lady Macbeth faints and has to be carried out of the room.  This is ironic because she is certainly aware that the king is dead; she must faint in order to play the part of the "gentle lady" that is expected of her.

The answer you are looking for can be found in Act II scene 2 of this great tragedy, which is of course the scene during which the murder takes place. Interestingly, however, Shakespeare chooses to focus on the action outside of the room where Duncan sleeps, and so we are able to see Macbeth and Lady Macbeth before and after the murder and see how they are psychologically impacted by the crime.

What is interesting to note is that Lady Macbeth, who up until this point has been so resolute and the one who has had to persuade her husband to commit the crime, now shows one moment of weakness. She herself tells us that she would have killed Duncan herself, but for the way that she was struck by his resemblance to her own father as he lay there sleeping:

Had he not resembled

My father as he slept, I had done't.

Thus we see that Lady Macbeth is not necessarily as evil and as lacking in compassion as we would guess from her behaviour and speech up until this point in the play.

At the beginning of Act 2, Scene 2, Lady Macbeth has evidently returned from Duncan's chamber. It is not clear whether she had been there before. She had to give Duncan's guards something to drug them and also lay out their daggers so that her husband could use them to kill Duncan. The idea is to plant the guards' blood-stained daggers on them and frame them for the murder. It is hard to see how Lady Macbeth could accomplish both tasks in one visit--drugging the guards and laying out their daggers for her husband. At any rate, she say Duncan sound asleep in his bed. She tells herself:

Had he not resembled
My father as he slept, I had done't.

She may or may not be rationalizing. After all, she has had no experience in killing people, whereas her husband has killed many. Why not leave the job to an expert? Her statement that she might have killed Duncan if he hadn't seemed to resemble her own father may be only Shakespeare's way of explaining why Lady Macbeth, who had the opportunity to commit the murder, didn't do it. Shakespeare may have intended to make this woman a more three-dimensional character. She is a woman, after all, and has a woman's feelings. She seems vicious and determined when talking to her husband, but when she is alone in Act 2, Scene 2, she reveals her doubts and fears.

Alack, I am afraid they have awaked,
And 'tis not done. Th' attempt, and not the deed,
Confounds us. Hark!

It would seem that Macbeth and his wife need each other. They give each other confidence. When they are separated, as they are at first in Act 2, Scene 2, they both become anxious and uncertain. It is to be observed that this is often the case with people who commit violent crimes, like the two young killers in Truman Capote's novel In Cold Blood. Separately these two young men would never have committed their horrible murders, but together they become a lethal pair, like two chemicals that are innocuous separately but volatile when mixed together. Macbeth would never have murdered Duncan if his wife hadn't pressured him to do it, and she needed her husband not only to bolster her nerve but to make the deed worth doing. She cannot become queen unless her husband becomes king. 

Lady Macbeth had plenty of opportunity to kill King Duncan and didn't do it. Maybe it was because the old man reminded her of her father, and maybe that is only her excuse for not being able to commit such a bloody deed because she didn't have enough nerve. 

It is Lady Macbeth who drives the plan to kill King Duncan. When Macbeth's will to murder Duncan fails, she goads him into carrying through the plans she has so carefully crafted. It is her plan to drug Duncan's attendants and lay out the daggers that her husband then will use in committing the crime. At the appointed hour, Lady Macbeth carries out her duties smoothly. After leaving Duncan's chamber, she remarks, some feel oddly, that she would have killed Duncan herself, except that as he slept, he resembled her father. This reference to her father, suggesting that she had loved him, adds an unexpected aspect to her character. Until this moment, Lady Macbeth had been portrayed as scheming, ambitious, cruel, and cold. No further reference in the play expands upon her statement, but Lady Macbeth's emotional disintegration in Act V confirms that she was not as impervious to human emotions as she had once seemed.