Difficult to say, really.
THe idea of murdering Duncan occurs to Macbeth before Lady Macbeth is even introduced into the play: just after he's heard the witches prophesy that he will be king, he soliloquizes:
...Why do I yield to that suggestion
Whose horrid image doth unfix my hair
And make my seated heart knock at my ribs,
Against the use of nature?
He's thinking about a murder. No prizes for guessing whose. And he writes to Lady M to tell his "dearest partner of greatness" about the prophecies. She resolves to get him "the golden round" which he is promised. And she seems to rather take over the plan, organising the means, the method, and the how-to of murdering Duncan. But Macbeth had the idea already.
The one point where she does seem key is in Act 1, Scene 7, when Macbeth backs out of the murder altogether, and she launches a ferocious assault on his manhood, on his honour, and finally, plays the card of their (recently deceased) child:
I have given suck, and know
How tender ’tis to love the babe that milks me.
Macbeth is back on board. He does the murder.
And then after that, it's Macbeth's game. She, in fact, is isolated from his decisions and his life: he doesn't ever tell her about Banquo's murder. Act 3, Scene 2 shows him openly rebutting her.
How responsible is she? Well, she has no influence late in the play, but she might well have some early on. How much? Would he have done it without her? Impossible precisely to say.
I think that she is at least partly responsible for his actions. When Macbeth leaves the table at the banquet in Act 1, Scene 7 and says that he can't kill Duncan, it is Lady Macbeth who persuades him to go through with the plan. She tries to make him feel guilty by saying "What beast was't then, that made you break this enterprise to me?", and it works.
Lady Macbeth: Glamis thou art, and Cawdor, and shalt be
wouldst be great;
ambition, but without
illness should attend it. What thou wouldst highly,
Hie thee hither,
chastise with the valor of my tongue
impedes thee from the golden round,(25)
metaphysical aid doth seem
it looks fairly clear to me how responsible she is. She says she'll bully him into regicide and then she does so. He would not have done it without her.
because she was the won who told macbeth to kill people and so they both did.