The Devil is doing all the work. But he is kept a slave by the error of man. He actually wants to unite with God. I really like Dostoevsky's take on this from The Brothers Karamazov. Jesus prays for all sinners. The Devil appears to Ivan the atheist:
"Yes, I am in my natural shape. For what am I on earth but a poor relation? By the way, I am listening to you and am rather surprised to find you are actually beginning to take me for something real, not simply your fancy, as you persisted in declaring last time--"
"Never for one minute have I taken you for reality," Ivan cried with a sort of fury. "You are a lie, you are my illness, you are a phantom. It's only that I don't know how to destroy you and I see I must suffer for a time. You are my hallucination. You are the incarnation of myself, but only of one side of me ... of my thoughts and feelings, but only the nastiest and stupidest of them. From that point of view you might be of interest to me, if only I had time to waste on you--"
"Scolding you, I scold myself," Ivan laughed again, "you are myself, myself, only with a different face. You just say what I am thinking ... and are incapable of saying anything new!"
"Well, that's how it is now, though I am your hallucination, yet just as in a nightmare, I say original things which had not entered your head before. So I don't repeat your ideas, yet I am only your nightmare, nothing more."
And the Devil makes his case, and explains his origins:
"God preserve me from it, but one can't help complaining sometimes. I am a slandered man. You upbraid me every moment with being stupid. One can see you are young. My dear fellow, intelligence isn't the only thing! I have naturally a kind and merry heart. 'I also write vaudevilles of all sorts.' You seem to take me for Hlestakov grown old, but my fate is a far more serious one. Before time was, by some decree which I could never make out, I was pre-destined 'to deny' and yet I am genuinely good-hearted and not at all inclined to negation. 'No, you must go and deny, without denial there's no criticism and what would a journal be without a column of criticism?' Without criticism it would be nothing but one 'hosannah.' But nothing but hosannah is not enough for life, the hosannah must be tried in the crucible of doubt and so on, in the same style. But I don't meddle in that, I didn't create it, I am not answerable for it. Well, they've chosen their scapegoat, they've made me write the column of criticism and so life was made possible. We understand that comedy; I, for instance, simply ask for annihilation. No, live, I am told, for there'd be nothing without you. If everything in the universe were sensible, nothing would happen. There would be no events without you, and there must be events. So against the grain I serve to produce events and do what's irrational because I am commanded to. For all their indisputable intelligence, men take this farce as something serious, and that is their tragedy. They suffer, of course ... but then they live, they live a real life, not a fantastic one, for suffering is life. Without suffering what would be the pleasure of it? It would be transformed into an endless church service; it would be holy, but tedious. But what about me? I suffer, but still, I don't live. I am x in an indeterminate equation. I am a sort of phantom in life who has lost all beginning and end, and who has even forgotten his own name.
I am perhaps the one man in all creation who loves the truth and genuinely desires good. I was there when the Word, Who died on the Cross, rose up into heaven bearing on His bosom the soul of the penitent thief. I heard the glad shrieks of the cherubim singing and shouting hosannah and the thunderous rapture of the seraphim which shook heaven and all creation, and I swear to you by all that's sacred, I longed to join the choir and shout hosannah with them all. The word had almost escaped me, had almost broken from my lips ... you know how susceptible and esthetically impressionable I am. But common sense--oh, a most unhappy trait in my character--kept me in due bounds and I let the moment pass! For what would have happened, I reflected, what would have happened after my hosannah? Everything on earth would have been extinguished at once and no events could have occurred. And so, solely from a sense of duty and my social position, I was forced to suppress the good moment and to stick to my nasty task. Somebody takes all the credit of what's good for Himself, and nothing but nastiness is left for me. But I don't envy the honor of a life of idle imposture, I am not ambitious. Why am I, of all creatures in the world, doomed to be cursed by all decent people and even to be kicked, for if I put on mortal form I am bound to take such consequences sometimes? I know, of course, there's a secret in it, but they won't tell me the secret for anything, for then perhaps, seeing the meaning of it, I might bawl hosannah, and the indispensable minus would disappear at once, and good sense would reign supreme throughout the whole world. And that, of course, would mean the end of everything, even of magazines and newspapers, for who would take them in? I know that at the end of all things I shall be reconciled. I, too, shall walk my quadrillion and learn the secret. But till that happens I am sulking and fulfill my destiny though it's against the grain--that is, to ruin thousands for the sake of saving one. How many souls have had to be ruined and how many honorable reputations destroyed for the sake of that one righteous man, Job, over whom they made such a fool of me in old days! Yes, till the secret is revealed, there are two sorts of truths for me--one, their truth, yonder, which I know nothing about so far, and the other my own. And there's no knowing which will turn out the better...
Well to begin I have to say that the types only pertain to natural beings, not the supernatural.
That being said I see him as an extrovert, as we know he convinced what? A third of heavens armies to rebel against God? I see INFJs and for that matter INTJs to rise form the ranks within and take control by less dramatic but more decisive means.
Honestly It's quite clear from what we know, despite his cleverness Lucifer lacks tacked. But I can't say what type he represents.