What part does lady Macbeth play Macbeth's decision to kill the king?

Her part is decisive. If you read or watch Act 1 Scene 7 you will know that Macbeth, left on his own, decided not to commit the murder. He says "We shall proceed no further in this business." Lady Macbeth then proceeds to change his mind, at least for long enough that the deed gets done. She appeals to his irrational emotions, when his decision not to commit the murder was based on reason and logic, as shown in Macbeth's speech, "If it were done when 'tis done, then 'twere well it were done quickly."