I want to give a hint to Robin Hartwell's remarkable essay: Threats and Promises: Lucifer, Hell, and Stockhausen’s SUNDAY from LIGHT, in: Perspectives of New Music 50, 2012, S. 393 – 424. Robin deals with the question, why Lucifer to a great extent is eliminated from the last opera of the LICHT-cycle. When we look at the superformula, that structures the cycle, that should not happen, and therefore when already composing SONNTAG Stockhausen had a plan to let appear Lucifer in that last opera. Regarding the spiritual content of the work it is clear that Lucifer cannot take part in the main plot, which is the mystical unification of Michael and Eve. But there was the plan to ban Lucifer in a prison, the so called "Luciferium", some special hell, and Stockhausen made some sketches to outline the composition of the Luciferium. But finally he never tackled that task. Why not? The author of this essay very clearly exposes the problem, interprets some sketches of the composer and considers certain possibilities to answer the question. I remember long discussions about this item in 2002 and the following years in Kürten; I myself was especially unhappy about the way Lucifer seemed to be treated here and had the suspicion that Stockhausen would fall back against what already was achieved in MITTWOCH, where Lucifer was integrated. My suspicion was that the dark sides of life finally were desintegrated in favor of a pink-coloured world of wishfull thinking, to put it briefly.
Robin finally comes to a very beautiful solution. To reach it he dives deeply into theological theories of our time. First he comes to Karl Barth who in the 20th century has renewed the old theory of apocatastasis: Finally everything and everybody will be redeemed in the light of God's love and grace and the only person that is sentenced to death is Christ himself. And then he recalls the position of Hans Urs von Balthasar, the catholic theologian, who sticks to the hope of universal salvation. Robin invites us to detect this in HOCH-ZEITEN: Lucifer appears here very in the background with parts of his formula, he is integrated in the multitude of voices at God's throne, not longer compells himself to play the special role of opposition and evil - and in this way at the very end of the piece he can without any problem sing the "b", that belongs to his formula, together with all the other pitches of the other voices. There is some speculation in that solution, but I like it, and it adds to the work a spiritual beauty and depth - I think Stockhausen would have nodded to this motive!

Indeed it is a very elegant explanation of Lucifer's position in SONNTAG. In reply to your question about why Stockhausen never composed the Luciferium, I recall Richard Toop saying once that Stockhausen told him it was simply a matter of not having a commission for it. Perhaps it is that simple although, according to the sketch, the Luciferium would last the entire length of SONNTAG. It is difficult to imagine a single singer sustaining such a long performance, even with the assistance of seven trombones, organ, and percussion. In the end, Stockhausen may have decided it just wasn't a very good idea.

In his article, Robin Hartwell expresses his belief that SONNTAG represents the Last Judgment, and in that sense is truly the "end" of LICHT, despite Stockhausen's insistence that there is neither beginning nor end to the week, and therefore also for LICHT. Richard Toop has also said he thinks Stockhausen must have changed his conception as work on the cycle approached completion, and that only three of the operas could conceivably serve as "conclusion". SONNTAG is one obvious candidate, and Richard said MITTWOCH is another, but I cannot remember him saying what the third candidate might be. Does anyone have opinions on this? Personally, I prefer Stockhausen's original position, according to which SONNTAG prepares for the new birth of MONTAG, and the Operator's fade-away at the end of MITTWOCH forecasts Michael's incarnation in DONNERSTAG, and I see nothing at all in SONNTAG that even suggests the Last Judgment—the third act of DONNERSTAG seems to be a closer match, in my opinion.

I think you can see that Stockhausen's view on Lucifer was very much inspired by the Urantia Book papers 53 and 54, even by 1:1 quotations.
So perhaps it helps to know what the UB tells about the destiny of Lucifer after havig lost the fight against Michael:

Paper 53 ("The Lucifer Rebellion"), section 9: Present Status of the Rebellion

(611.4) 53:9.5 Since Michael’s final bestowal no one in all Satania has desired to go to the prison worlds to minister to the interned rebels. And no more beings have been won to the deceiver’s cause. For nineteen hundred years the status has been unchanged.

(611.5) 53:9.6 We do not look for a removal of the present Satania restrictions until the Ancients of Days make final disposition of the archrebels. The system circuits will not be reinstated so long as Lucifer lives. Meantime, he is wholly inactive.

(611.6) 53:9.7 The rebellion has ended on Jerusem. It ends on the fallen worlds as fast as divine Sons arrive. We believe that all rebels who will ever accept mercy have done so. We await the flashing broadcast that will deprive these traitors of personality existence. We anticipate the verdict of Uversa will be announced by the executionary broadcast which will effect the annihilation of these interned rebels. Then will you look for their places, but they shall not be found. “And they who know you among the worlds will be astonished at you; you have been a terror, but never shall you be any more.” And thus shall all of these unworthy traitors “become as though they had not been.” All await the Uversa decree.

So there are two messages about Lucifer:
- He is "wholly" inactive" and
- the universe waits for the "annihilation of these interned rebels. Then will you look for their places, but they shall not be found."
I ask myself, whether these are the reasons why Lucifer has no importance in SONNTAG - he "shall not be found"...

Yes, good observation. However, if Lucifer "shall not be found" in SONNTAG, why is he present in all of the other LICHT operas (except possibly MITTWOCH)? If we accept that the other six operas represent a period prior to the quashing of the Lucifer Rebellion and SONNTAG comes afterward, we are necessarily saying that indeed the week, and LICHT, has a beginning and an ending: its content exists "in time". This has to do precisely with the question I asked about whether Stockhausen changed his mind about the nature of LICHT as it was nearing completion. The banishment of Lucifer to the Luciferium could be interpreted as evidence in favour of this view but, in the end, Stockhausen did not do this, and Lucifer's formula does in fact return toward the end of SONNTAG, as Robin points out in his article. This is why apocatastasis is such a compelling explanation, though in fact it is in opposition to the papers from the Urantia Book which you cite here, which in no way suggest the possibility of any such "restoration" for Lucifer. In fact, I would go so far as to say that apocatastasis in SONNTAG permits the cycle to continue into MONTAG.

Perhaps we must make a difference between Lucifer as a personality (not present in SONNTAG) and the Luciferian principle, which appears as the Lucifer formula. The Urantia Book doesn't claim that with the end of Lucifer's rebellion the sin and the evil would have stopped to exist - it would be foolish to do so. The UB instead claims quite clearly (in paper 54 p.ex.) that the capability of men to chose between good and evil is a universal reality and even a condition for freedom of evolution which is the basic principle of the universe. So with every human being who has the capacity to decide to listen to or to deny his divine Thought Adjuster, the cosmic drama of divine order and rebellion begins again. This explains why after SONNTAG there can be a MONTAG again and again, even if Lucifer is imprisoned. His arguments are not!

Does that mean (in the logic of the Urantia Book) that another Lucifer could arise - maybe with another name? That leads to the remark, that (for Stockhausen at least) not Lucifer as personality is important (he is only secondary) but the "principle", what means in the operas: the formula. That is what matters, and it is not so important if he appears personally or not.

Following the Urantia Book, there is "another Lucifer", named Caligastia. He is mentioned in UB paper 53, section 1, and there it is said that he is the so-called devil:
(602.1) 53:1.4 Very little was heard of Lucifer on Urantia owing to the fact that he assigned his first lieutenant, Satan, to advocate his cause on your planet. Satan was a member of the same primary group of Lanonandeks but had never functioned as a System Sovereign; he entered fully into the Lucifer insurrection. The “devil” is none other than Caligastia, the deposed Planetary Prince of Urantia and a Son of the secondary order of Lanonandeks. At the time Michael was on Urantia in the flesh, Lucifer, Satan, and Caligastia were leagued together to effect the miscarriage of his bestowal mission. But they signally failed.

In paper 66, sect. 1, we learn:
(741.3) 66:1.1 Caligastia was a Lanonandek Son, number 9,344 of the secondary order. He was experienced in the administration of the affairs of the local universe in general and, during later ages, with the management of the local system of Satania in particular.

(741.4) 66:1.2 Prior to the reign of Lucifer in Satania, Caligastia had been attached to the council of the Life Carrier advisers on Jerusem. Lucifer elevated Caligastia to a position on his personal staff, and he acceptably filled five successive assignments of honor and trust.

(741.5) 66:1.3 Caligastia very early sought a commission as Planetary Prince, but repeatedly, when his request came up for approval in the constellation councils, it would fail to receive the assent of the Constellation Fathers. Caligastia seemed especially desirous of being sent as planetary ruler to a decimal or life-modification world. His petition had several times been disapproved before he was finally assigned to Urantia.

(741.6) 66:1.4 Caligastia went forth from Jerusem to his trust of world dominion with an enviable record of loyalty and devotion to the welfare of the universe of his origin and sojourn, notwithstanding a certain characteristic restlessness coupled with a tendency to disagree with the established order in certain minor matters.

Caligastia was also the one Jesus met after his baptism, see paper 136, sect. 3:
(1512.5) 136:3.1 Jesus had endured the great temptation of his mortal bestowal before his baptism when he had been wet with the dews of Mount Hermon for six weeks. There on Mount Hermon, as an unaided mortal of the realm, he had met and defeated the Urantia pretender, Caligastia, the prince of this world. That eventful day, on the universe records, Jesus of Nazareth had become the Planetary Prince of Urantia. And this Prince of Urantia, so soon to be proclaimed supreme Sovereign of Nebadon, now went into forty days of retirement to formulate the plans and determine upon the technique of proclaiming the new kingdom of God in the hearts of men.

The most important question, however, is: What is Caligastia's role today? Is he still active? Or is he imprisoned like Lucifer? The UB gives an interesting answer in paper 53, sect. 8:
(610.2) 53:8.6 (...) Caligastia, your apostate Planetary Prince, is still free on Urantia to prosecute his nefarious designs, but he has absolutely no power to enter the minds of men, neither can he draw near to their souls to tempt or corrupt them unless they really desire to be cursed with his wicked presence.

(610.3) 53:8.7 Before the bestowal of Michael these rulers of darkness sought to maintain their authority on Urantia, and they persistently withstood the minor and subordinate celestial personalities. But since the day of Pentecost this traitorous Caligastia and his equally contemptible associate, Daligastia, are servile before the divine majesty of the Paradise Thought Adjusters and the protective Spirit of Truth, the spirit of Michael, which has been poured out upon all flesh.

(610.4) 53:8.8 But even so, no fallen spirit ever did have the power to invade the minds or to harass the souls of the children of God. Neither Satan nor Caligastia could ever touch or approach the faith sons of God; faith is an effective armor against sin and iniquity. It is true: “He who is born of God keeps himself, and the wicked one touches him not.”

(610.5) 53:8.9 In general, when weak and dissolute mortals are supposed to be under the influence of devils and demons, they are merely being dominated by their own inherent and debased tendencies, being led away by their own natural propensities. The devil has been given a great deal of credit for evil which does not belong to him. Caligastia has been comparatively impotent since the cross of Christ.

By the way: The UB also says that this is the reason why demons really existed and could possess men at the time of Jesus but aren't able anymore to do so since Pentecost. So exorcism was right in the days of Jesus but it is nonsense today, the UB teaches.
Sorry for that long answer...