So which is it? Was Satan lying? Or is he the god of this world so that he really did possess all of those kingdoms he offered Jesus?
He may have been lying, or because of his arrogant, pompous nature he may have convinced himself that he possessed those kingdoms. Human beings with such natures can be self-deceived and are incapable of facing reality. I wouldn't be surprised if that had been the case with Satan also.
According to the second century Christian writer, Irenaeus, there is only one "God of this world" and that is GOD! People have ascribed the reading from 2 Corinthians to some other god, or to Satan, because they have misread Paul. In Greek, the phrase "the God", if not qualified by other words refers to the one and only God. Irenaeus believes "of this world" does not qualify "the God" but qualifies "them which believe not."
Irenaeus also relates another passage in which the modifiers are in the wrong place. The passage reads as if Christ's coming is after the working of Satan, etc., but the reference actually is not to Christ but to "the wicked one."
[Christ] shall destroy [the wicked one] with the presence of his coming whose coming is after the working of Satan with all power and signs and lying wonders II Thessalonians 2:9
From Irenaeus (120-202 A.D.) Book 3 AGAINST HERESIES
1. As to their affirming that Paul said plainly in the Second [Epistle] to the
Corinthians, “In whom the god of this world hath blinded the minds of
them that believe not,†and maintaining that there is indeed one god of this
world, but another who is beyond all principality, and beginning, and
power, we are not to blame if they, who give out that they do themselves
know mysteries beyond God, know not how to read Paul. For if any one
read the passage thus  according to Paul’s custom, as I show elsewhere,
and by many examples, that he uses transposition of words  “In whom
God,†then pointing it off, and making a slight interval, and at the same
time read also the rest [of the sentence] in one [clause], “hath blinded the
minds of them of this world that believe not,†he shall find out the true
[sense]; that it is contained in the expression, “God hath blinded the minds
of the unbelievers of this world.†And this is shown by means of the little
interval [between the clause]. For Paul does not say, “the God of this
world,†as if recognizing any other beyond Him; but he confessed God as
indeed God. And he says, “the unbelievers of this world,†because they
shall not inherit the future age of incorruption. I shall show from Paul
himself, how it is that God has blinded the minds of them that believe not,
in the course of this work, that we may not just at present distract our
mind from the matter in hand, [by wandering] at large.
2. From many other instances also, we may discover that the apostle
frequently uses a transposed order in his sentences, due to the rapidity of
his discourses, and the impetus of the Spirit which is in him. An example
occurs in the [Epistle] to the Galatians, where he expresses himself as
follows: “Wherefore then the law of works? It was added, until the seed
should come to whom the promise was made; [and it was] ordained by
angels in the hand of a Mediator.†For the order of the words runs thus:
“Wherefore then the law of works? Ordained by angels in the hand of a
Mediator, it was added until the seed should come to whom the promise
was made,† man thus asking the question, and the Spirit making answer.
And again, in the Second to the Thessalonians, speaking of Antichrist, he
says, “And then shall that wicked be revealed, whom the Lord Jesus
Christ shall slay with the Spirit of His mouth, and shall destroy him with
the presence of his coming; [even him] whose coming is after the working
of Satan, with all power, and signs, and lying wonders.†Now in these
[sentences] the order of the words is this: “And then shall be revealed that
wicked, whose coming is after the working of Satan, with all power, and
signs, and lying wonders, whom the Lord Jesus shall slay with the Spirit
of His mouth, and shall destroy with the presence of His coming.†For he
does not mean that the coming of the Lord is after the working of Satan;
but the coming of the wicked one, whom we also call Antichrist. If, then,
one does not attend to the [proper] reading [of the passage], and if he do
not exhibit the intervals of breathing as they occur, there shall be not only
incongruities, but also, when reading, he will utter blasphemy, as if the
advent of the Lord could take place according to the working of Satan. So
therefore, in such passages, the hyperbaton must be exhibited by the
reading, and the apostle’s meaning following on, preserved; and thus we do
not read in that passage, “the god of this world,†but, ââ¬Å“God,†whom we do
truly call God; and we hear [it declared of] the unbelieving and the blinded
of this world, that they shall not inherit the world of life which is to come.