Luk 11:3 Give us day by day our daily bread.
This loaf of ours, the one sufficient for the coming day, give to us, the one during the course of a day.
The KJV translation reverses the word order of the Greek. This is important because Greek word order is important. Generally, the most important words appear first in a phrase in Greek because they are not bound to the subject-verb-object order of English. This verse contains another a very rare word, the meaning of which is debatable.
The Greek word translated as "give" means "to give" and "to grant. This verb appears in the middle of the sentence rather than at the beginning. It is in a form which is used both for commands and requests in ancient Greek. Unlike the verse in Matthew (Matthew 6:11), where the tense was "at some time", the tense here is the present.
Three Greek words are translated as "day by day" but they mean "the one during the course of a day". The "the one" comes from the Greek article, "the," which usually proceeds a noun and, without a noun, takes the meaning of "the one." The "during the course of" comes from a preposition that means "down from", "down into", "against", "opposite", and so one, but with a measurement of time, it means "during the course of a period." The Greek noun translated as "day" also means "day", "time," in general, and refers specifically to the "daytime." This "day" only occurs once.
The Greek word translated as "this day" is not a noun or any combination of a demonstrative pronoun and a noun. It is an adverb. It means "for the day" or "to the day." This word appears at the very end of the sentence.
The word translated as "daily" is an adjective modifying "bread" but it is used as a noun. We know this because it is introduced by an article, "the". Though translated as "daily," this adjective is only used very rarely in Greek, so rarely that its meaning is debatable. This use was clearly intentional, meant to get most people wondering what was meant. In the Gospels, it is used once here in Luke and again in Matthew's version of the Lord's prayer. It is thought to mean "sufficient for what is coming" based on a possible root word that means "to come on, to approach." If Jesus had meant "daily," he would have used another word based on the Greek word for "day", a form of the word "day" above. See this article for a complete historical discussion of this word.
Assuming that Christ meant the specific meaning of the word describing the bread as "sufficient for what is coming," the word becomes an announcement that something new is coming, but, of course, that was also the message of the line in Mat 6:10.
The word translated as "bread" means a "loaf" of a specific type of bread, but it is translated consistently throughout the NT as "bread."
The use of a rare word meaning "sufficient for what is coming" to describe the bread requested in the prayer.
τὸν ἐπιούσιον (adj sg neut acc) "Daily" is from epiousios, which may mean "sufficient for the coming day"," "sufficient for the current day", and "for the day" but it very rarely appears elsewhere besides here and Matthew. It could be from the verb epiousa, which means "to come on, to approach." It may also be from epi eimi, meaning literally "upon being" or "being upon". The Greek word for "daily" is hêmerousios, the adjective form of hemera, the Greek word for "day", a form of which ends this sentence. "Hemero-" is a common prefix meaning a day's supply of something.
τὸ (article sg neut acc) (article) Untranslated is the Greek article, "the," which usually proceeds a noun and, without a noun, takes the meaning of "the one" or, in the plural, "the ones." Here it is separated from its noun by a conjunction. -
καθ᾽ (prep) "By" is kata, which, as a preposition, means "downwards", "down from", "down into", "against", "down toward", "opposite", "separately", "individually", "at a time", "towards", "in accordance with", "concerning", "corresponding with", "during the course of a period," and "severally." As an adverb, it means "according as", "just as", "in so far as", "wherefore", "like as if" and "exactly as."
ἡμέραν: (noun sg fem acc) "Day" is hemera, which, as a noun, means "day" "a state or time of life", "a time (poetic)", "day break" and "day time." It is also and also has a second meaning, of "quiet", "tame (animals)", "cultivated (crops)," and "civilized (people)."