I wanted to add to this thread some other things I find interesting about the possible association between the deaths and resurrections of Lazarus and Jesus and initiation.
I've already pointed out that the two mourning sisters of Lazarus remind me of the two mourning sisters of Osiris - Isis and Nepthys. I'm also reminded of the mourning women at Jesus's crucifixion and the women who go to his tomb to anoint his corpse.
During the Egyptian resurrection ritual women would play the role of the mourning sisters and sometimes mother(Nut) of Osiris while the lector priest performs the resurrection ritual.
The Mortuary Papyrus of Padikakem Walters Art Museum 551(ISD LLC, Dec 31, 2011), Yekaterina Barbash:
Section 1 is a ritual addressed to Osiris and said to be recited by Isis, Nut, Nepthys, and a crowd of "men and women". Section 2 is a compilation of glorification spells to be spoken by the lector priest for the deceased Padikakem, the assumed owner of the manuscript...
Both compositions of papyrus W551 are mortuary in character and address Osiris or the deceased associated with him... Thus while section 1 contains earthly expressions of love and mourning for the deceased, section 2 deals with his transition to a new state of being in the hereafter. The sequence of the texts corresponds with the Egyptian perception of death, i.e., the deceased is gradually transformed after death, from this world to the sphere of the divine...
The corpus of "s3hw" spells was concerned with elevating Osiris and/or the deceased to a new state of existence and should be understood as a
category of Egyptian mortuary literature... The lamentations bring about the revitalization of Osiris by means of mourning itself. The two goddesses, Isis and Nepthys, refer to death from the viewpoint of the living, uncovering their human emotions, as they recall their love for Osiris and grieve for him. On the contrary, glorifications tend to deal with death from a more mythological perspective of the hereafter. Thus, unlike the earthly pleas of Isis and Nepthys, the myth of Osiris, Horus, and Seth is evoked in spell 10 of PW 551:"The Great One(=Osiris) awakens, The Great One wakes up. Osiris raised himself on his side, the One who hates sleep (i.e., death), one who does not love weariness. The god stands, being powerful of his body. Horus has lifted him up, he's raised in Nedit."... In the s3hw as well as in other mortuary texts such as the BR, the transformation into an akh accurs by means of association of the deceased with the god Osiris and his incorporation into the sphere of the divine...
Similarly, Osiris' mother, Nut, functions mainly as the protector in his time of vulnerability and rejuvenation, as for example in spell 5 of PW 551: "Your mother, Nut, has spread herself over you... She protected you of all evil things". Her motherly role is repeatedly stressed throughout the composition... Isis and Nepthys perform the widest range of tasks for the deceased Osiris, including purification, protection, and reassembling. At the same time, the two sisters act as they do in the lamentations, mourning and "glorifying" Osiris...
Notice in the bolded part of the quote above the deceased/Osiris is said to be asleep but will wake up.
John 11:
After saying this, he told them, “Our friend Lazarus has fallen asleep, but I am going there to awaken him.” 12 The disciples said to him, “Lord, if he has fallen asleep, he will be all right.” 13 Jesus, however, had been speaking about his death, but they thought that he was referring merely to sleep. 14 Then Jesus told them plainly, “Lazarus is dead. 15 For your sake I am glad I was not there, so that you may believe. But let us go to him.”
So you have Jesus in the role of Horus/the lector priest, Lazarus in the role of Osiris/the deceased, and the mourning sisters in the role of Isis and Nepthys.
Continuing with The Mortuary Papyrus of Padikakem Walters Art Museum 551:
Although s3hw primarily associate the deceased with Osiris, the latter's nightly union with Re results in a solid connection of the deceased with the sun god. The transformation of the deceased into the new state of existence as an akh can be equated with the cyclical process of the sun, as it is newly born and rises each morning... Cruz-Uribe points out that all the rooms in Theban mortuary temples containing mortuary spells also involve themes of the rebirth of the sun god, Re-Horakhty. The gods Re and OSiris unite into a giant, omnipresent deity who spans the sky and the netherworld...
In other words, transformation into a god was a necessary part of assimilation into the Netherworld... s3hw were specifically designed to transform and restore the social functions as well as the physical body of the deceased through the connection with the sphere of the divine.
All the rituals performed in Egyptian mortuary literature and by the pharaoh during his inauguration are associated with the death and resurrection/rebirth of either Osiris or the sun god. The deceased and the living pharaoh are ritually identified with a deity that dies and is reborn/resurrected.
The mortuary texts are constantly referred to as "initiations into the mysteries of the Netherworld" and the "mystery" is always associated with Osiris and the sun god. Part of this initiation was a purification in the waters of the netherworld called "Nun". Just as the sun god enters the waters and is reborn, so is the initiate.
‘The Social and Ritual Context of a Mortuary Liturgy of the Middle Kingdom (CT Spells 30-41)', in: H. Willems (ed.),
Social Aspects of Funerary Culture in the Egyptian Old and Middle Kingdoms. Proceedings of the International Symposium Held at Leiden
University, 6-7 June, 1996, Orientalia Lovaniensia Analecta 103 (Leuven, 2001), p. 253-372:
Osiris is said to give orders to let the deceased enter his shrine... Prior to this, the deceased is said to be purified in the Jackal-lake and in the Lakes of the Dwellers in the Netherworld... The "Lake(s) of the Jackal(s)" and the "Lake(s) of the Dwellers of the Netherworld" occur frequently in the funerary literature, and they were clearly thought to be located near the Eastern horizon. In PT 372b the deceased is said to be washed there in a context also referring to the appearance of Re. It is likely that the lakes are here associated with the netherworldy pools where the sun god bathes prior to sunrise. Funerary texts often link this idea with navigations through the netherworld. Such navigations are frequently the topic of texts which also refer to purification in the two lakes under discussion... Immediately before, the same text points out that the deceased has been purified in the same lake as Osiris...
The implication of this hypothesis is that the journey of the deceased through the netherworld according to spell 36 is a netherwordly reflection of the Osiris mysteries performed on earth... The deceased will receive divine status in the House of the White Bull... The deceased will enter into the abode of Osiris.
A Journey Through the Beyond The Development of the Concept of Duat and Related Cosmological Notions in Egyptian Funerary Literature(ISD LLC, Feb 1, 2022), Silvia Zago
Moreover, at least some of these passages mentioning the lake(s) of the Duat associate these with the sun and the eastern horizon, near which such lakes may have been imagined to be located. In virtue of this connection, the Duat may be surmised to assume the connotation of a liminal, transitional place, where the sun and the king get cleansed before being ready to reappear on the horizon every morning and to rise in the sky. Ultimately, (ritual) purity was a necessary condition for being reborn, and for this reason it is often connected with the notion of the (initiatory) journey of the deceased through the Duat. The association between Osiris and water in a context of purification, renewal, and rebirth also had a long tradition in ancient Egyptian (funerary) literature...
The Egyptian Book of the Dead: The Book of Going Forth by Day edited by Eva Von Dassow:
Every evening the aged sun entered the underworld and travelled through it, immersed in Nun, only to emerge at dawn as Khepri, the newborn sun. Thus, the waters of Nun had a rejuvenating, baptismal quality essential to rebirth.
Finally the initiation ends with a sacred meal between the newly transfigured initiate and the gods of the netherworld.
Death and Initiation in the Funerary Religion of Ancient Egypt, Jan Assmann in Religion and Philosophy in Ancient Egypt, Yale Egyptological
Studies 3, 1989, S. 135-159:
Membership in this community is the only way for the deceased to partake of the sustenance of the gods; it is, on the other hand, the sharing in the divine nourishment which makes him a member of the community of gods. This specific motif appears repeatedly as a sacramental explanation in those spells concerned with the concrete action of eating and drinking...
Thy bread is the bread of Re,
thy beer is the beer of Hathor.
Thou getest up and siteth down for thy meal
and joinest the gods who follow the god (Re).
The means and the end are fully interchangeable: eating and drinking (a social act of paradigmatic significance) are the ideal concretizations of the desired social integration, while social integration inversely represents the prerequisite for sustenance in the hereafter...
A truly righteous one.
Let him be given the bread and beer,
which issues forth from Osiris.
He shall be forever amongst the followers of Horus...
In the second century text "The Golden Ass" by Apuleius, the initiate into the mysteries of Isis goes through a water purification, a death and rebirth ritual, and ends it all with a sacred meal. The description of the initiates experience is pretty much exactly what the deceased and sun god go through in the Egyptian Netherworld texts.
You also find this in other mystery cults and Christianity. I think Paul's idea of baptism as a death and rebirth ritual is probably influenced by the ritual of initiation. He combines the water purification with the death and rebirth ritual and then you eat a meal in remembrance of Jesus.