In the Ainulindalë Melkor chooses to follow his own will rather than the design of Ilúvatar and to usurp the act of creation (S 16-17). It's noteworthy here that in response Ilúvatar does not cast Melkor out, but tries to explain to him why he is unable to create independently and the harm that his attempt to do so has caused for the created world. Ilúvatar even allows Melkor to go down into the world on the pretext (advanced by Melkor) that he will work to repair the harm he has done. It seems entirely clear that Melkor could have repented in truth as he pretended to do. This true from the very beginning, appearing in The Book of Lost Tales (LT I 53-55, 57). We later see Aulë make a similar mistake in fashioning the Dwarves, but he is humble and repents when Ilúvatar speaks to him about it (S 43-44). Later still, even after all the evils he had committed in the First Age, repentance and a return to the fold was open even to Sauron (S 285).
Now Tolkien often compared the Valar and Maiar to the angels which are a part of the Christian religion. In the early days of the legendarium he even described them as gods. In The Book of Lost Tales I & II, for example, he refers to them in this way 319 times--yes, I counted*--which leads to a revealing contrast with his practice in his letters, where he almost always puts the word in quotations marks, 'gods,' or qualifies it with another word, 'roughly,' or phrase 'if you will.' Calling them 'gods' and likening them to angels often occur in the same letters and about the same number of times ('gods' 19; 'angels/angelic' etc. 20). When doing so Tolkien is being careful to make clear to readers not named Tolkien or Lewis that they are not really gods, but only gods so to speak. They occupy the mythological, not theological, place of gods (cf. Letters² #212 p. 405). So calling them 'gods' is also implicitly a comparison.
Just how much of a comparison it is we can see from how great a departure Tolkien is making from Christian doctrine with the Valar and Maiar. For it has long been doctrine that the fallen angels cannot repent, as Melkor pretends to do, Sauron almost does, and as Aulë succeeds in doing. The seeming glance to the West that the spirit of Saruman takes immediately after death shows that he believed repentance for him might be possible (RK 6.viii.1020). Being both fallen and dead, Saruman's answer is blowing in the wind.
In discussing fallen angels Saint Thomas Aquinas quotes Saint John Damascene to help make his point. Aquinas's quotation in the Summa Theologiae includes only the first of the two sentences below (ST 1 64.2). A fuller quotation of Saint John Damascene's De Fide Orthodoxa is illustrative (II.4):
“…hoc est hominibus mors, quod angelis casus. Post casum enim non est eis paenitentia, quemadmodum neque hominibus post mortem.”
Or, if your Latin's rusty:
“…death is to men what the fall is to angels. For after their fall there is no repentance for them, just as there is none for men after death.”
Aquinas says further that the fall of the angels happened not because they desired evil per se, but because they desired a good inordinately, thus placing their own will before God's (ST 1 63.1 ad 4): "et hoc modo angelus peccavit, convertendo se per liberum arbitrium ad proprium bonum, absque ordine ad regulam divinae voluntatis." "And in this manner the angel fell, by turning himself to a good of his own [which was determined] by his own free will, and out of order with the rule established by God's will."
Lucifer is presumably "the angel" Aquinas refers to here. So, too, Melkor desired to create things of his own according to his own design (S 16).
While Tolkien is clearly, obviously, and by his own admission, a very religious man whose faith and worldview play a great part in the way he shaped his legendarium, here is an instance where we can see that his mythology is not simply a reproduction of his theology. Just as making the Elves immortal and able to reincarnate allows him to examine human concerns about life and death in ways not possible otherwise, allowing for repentance among the "angels" affords still other possibilities that deserve to be noted and explored.
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*I count only instances in the text of The Book of Lost Tales I & II, or times when Christopher Tolkien quotes a different draft of his father's work. I do not count Christopher's own use of 'gods' in the notes and commentary; 'gods' in the notes and commentary that reproduces what has already been counted in the text; 'gods' when quoted from later works; or any of the front or back matter of The Book of Lost Tales