Allow me to build on the previous comments.
τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δὸς ἡμῖν σήμερον·
the bread of us for-[our]-sustenance give to us this day
I think you are onto something with the replacement of the usual translation, "daily" bread, which appears in the same sentence as "this day". This apparent redundancy is at odds with the unique term, in Greek, that is used to relay something special in this particular context.
That is to say, the redundancy is out of place. The unique word used ought to draw attention rather than be rendered superfluous.
In the same sentence, there is a common term that would not serve the same meaning as the unique term. Maybe it did not carry the full meaning of that unique term.
σήμερον sēmeron = "this day" or "today", as per 41 appearances in Scripture and many more instances of words of similar derivation.
This is a common term and does not resemble the other term used in the same sentence but which has only 2 appearances in Scripture.
The word, ἐπιούσιον, is a term that appears to have been coined for special use in the NT. Meanwhile, there are more common forms of "daily" that could have been used. This particular term, ἐπιούσιον, does not appear in any other context, nor elsewhere, in Greek versions of the Old or New Testaments nor in contemporaneous Greek literature. The context may provide the key to its meaning.
It appears to be unique to the Lord's prayer. The Greek text of Matthew and Luke used a term coined to express something special that Jesus had taught them, perhaps before or after this particular moment in his ministry.
For instance, the offered interpretation above is a term that seems quite clumsy to use in other biblical contexts precisely because it has been coined for this special context. That could explain why this Greek term does not appear elsewhere in the NT nor in other Greek texts of the time.
To wit: for-[our]-sustenance.
This translation/ interpretation might get at one basic meaning and perhaps hints of at least one other mystical meaning. Sustenance = necessities like physical nourishment. And sustenance = spiritual nourishment. But to relay either meaning or both meanings, it would not be necessary to coin such a word as this one. Everyday bread is familiar and so lends itself to being used metaphorically, for instance. Why coin a special word for everyday or daily bread?
The Greek term is unique because it is meant to transmit a unique meaning.
It might be better interpreted to fit its context whereby Jesus referred to himself as the bread that God sends from heaven. And, later, he linked back to this notion when he served bread at the Last Supper and, later again, after his resurrection. Keep in mind that the writers of these Gospels understood this context, special to the teachings and ministry of Jesus. They wrote to unfold that context for their audience even if, at the moment in each narrative, they were hinting or foretelling what was to come later.
The unique term: ἐπιούσιον
epi = super
ouison = substance/ substantial
And so: "super-substance: or "super-substantial bread". Or also super-necessity-essence.ousia = substance, (ousion)epiousion
In the Latin Vulgate, Jerome translated this Greek term ἐπιούσιον, with one Latin phrase in Luke and a different Latin phrase in Matthew. This suggests some uncertainty, perhaps.
Tὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δὸς ἡμῖν σήμερον·
Give us this day our super-substantial bread.
Panem nostrum supersubstantialem da nobis hodie,
Τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δίδου ἡμῖν τὸ καθ’ ἡμέραν·
Give us this day our daily bread.
Panem nostrum quotidianum da nobis hodie.
Both use the same opening with that unique word:
Τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον [...]
Give us this day our (ἐπιούσιον / epiousion) [...]
These are the only two appearances of this unique word, ἐπιούσιον.
Why would Jerome translate or interpret the same unique word differently in the same context?
The differences between the two NT passages are in the second part of the sentence:
||δὸς ἡμῖν σήμερον·
||δίδου ἡμῖν τὸ καθ’ ἡμέραν
||grant us today (this day)
||give to us each day (every day)
Not much difference there, but for possible nuance. Matthew imparts immediacy, the day on which the prayer is made. Luke imparts now and the future days on which the prayer is and will be made. Subtle differences but not huge in terms of the context of Jesus teaching his disciples a manner (or model) for prayer.
Okay, so here is how the two passages read without translation of the unique Greek term, ἐπιούσιον.
Τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δὸς ἡμῖν σήμερον·
The bread of ours (Our bread) (ἐπιούσιον/epiousion) grant us today.
Τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δίδου ἡμῖν τὸ καθ’ ἡμέραν·
The> bread of us (Our bread) (ἐπιούσιον/epiousion) give to us each day.
Seems to me that in the Lord's prayer, it is reasonable to insert something like super-substantial given the special context of bread from heaven and Jesus teaching that he is the bread God has sent from heaven. As they composed, the two Gospel writers understood that Jesus is the Word. And they used a term that perhaps one borrowed from the other because of the special meaning intended. Seems it was meant to impart a kind of bread that was essential -- more so than bread for physical nourishment, more than for spiritual encouragement, and thus very much particular to Jesus and his salvific role.
So here are the two passages fully translated:
Give us our super-substantial bread this day.
Grant us our super-substantial bread each day.
Matthew and Luke relayed the same meaning. But how to interpret the translation to reveal that special meaning?
This part of the Lord's prayer is a petition with three co-jointed meanings: for the necessities of life, for the God-given spiritual nourishment (the Word of God), and the foretelling of the Eucharist (Jesus himself).
It is written, Not in bread alone doth man live, but in every word that proceedeth from the mouth of God.
John 6, Jesus fed the multitude with a few loaves of bread.
56 He that eateth my flesh, and drinketh my blood, abideth in me, and I in him. 57 As the living Father hath sent me, and I live by the Father; so he that eateth me, the same also shall live by me. 58 This is the bread that came down from heaven. Not as your fathers did eat manna, and are dead. He that eateth this bread, shall live for ever.
Jesus took bread, and when he had given thanks, he broke it and gave it to his disciples, saying, “Take it; this is my body.”
In chapter 22 of the Gospel of John, the resurrected Jesus fed the Apostles with bread and they recognized him; he told Peter, "Feed my lambs" and "Feed my sheep".
[Note that the word, δίδου, appears only twice in the NT but there are many words that appear to be similarly derived, unlike the unique term, ἐπιούσιον.]