Abarim Publications' online Biblical Greek Dictionary
The verb λαγχανω (lagchano) means to get by luck: to establish, determine or obtain but specifically not by anybody's dedicated skill or deliberations but rather by lot, chance, fate or fortune (Luke 17:20). The core idea of monotheism is not the belief in one deity, but rather the understanding that all things made by the deity always work together (Romans 8:28). That means that the whole of evolving reality will draw toward the Logos (John 12:32), even when any individual element appears to be wildly off course (Matthew 26:24). Every person interacts with the whole of reality the way a fish swims in water: the water that is pushed out of the way will always find a way to push back at the fish, and no matter what an individual person decides to do, the whole of reality will always find a way to draw to God. This driving force that an individual experiences from reality at large is what the ancients called fate or lot.
An animal can't think outside his own box and identifies only with himself, his own will and his own experiences. But an enlightened person identifies with the larger whole (Luke 9:23, John 12:24, Galatians 2:20), and so does not have a localized animal mind but a global one and partakes in the divine nature (2 Peter 1:4). To such a person it doesn't really matter what happens to himself because all that matters is what happens to the whole of creation (Romans 8:19). Such a person will also understand that being born in an area of the world where one has an excellent chance of getting a formal education, and thus ending up wealthy and well informed, with enough spare time to pursue religion as a hobby and meet friends for one's weekly Bible study, does not make one a better or godly person, just a very lucky one, and rather a person tasked with spreading this joy (i.e. economic wealth) globally. Just like a global fire has to start with a single local flame, and it doesn't matter where that initial flame was (or where lightning first struck), so those of us that were among the first wave of saved fortunates, were saved by pure luck (2 Peter 1:1), and for the sole purpose of making the entire world as fortunate as we are (Romans 14:11).
Our verb λαγχανω (lagchano) is a rarer and more figurative synonym of verbal phrases involving the noun κληρος (kleros), which describes an actual physical lot, which was used for actual lotteries. Dividing properties and priestly duties by lottery was always common in Judaism, and later also in Athens, and marks the astonishing insight that reality is based on a foundation of unpredictability (quantum indeterminacy is self-similar to the autonomy of living beings and the free will of conscious minds).
In Greek mythology, one of the three Fates was named from our verb: Λαχεσις (Lachesis). From this same verb derives the noun ληξις (lexis), determination by lot, chance or fate, which is not used in the New Testament, but combined with the deified δικης (dike), justice, this word formed a formal law-term describing a charge filed: the first step in a legal proceeding. This is precisely the sentiment behind the familiar Latin phrase "alea iacta est", which literally translates as "the die is cast" but which rather means "come what may" (the verb iacio means to throw, let go, emit; hence also words like eject and project).
Our verb λαγχανω (lagchano) is thought to stem from an otherwise weakly attested Proto-Indo-European root "leng-", meaning to obtain. A creative speaker of Koine, however, may have realized that throwing a lot does not "obtain" anything (and certainly not the obscure will of a tyrannical deity), but rather creates determined data out of indetermined chaos in a collapsed wave function sort of way. Such creativity may also have linked our verb rather to a Proto-Indo-European root that has to do with being weak, loose or flappy: hence words like λαγαρος (lagaros), hollow or sunken, λαγαιω (lagaio), to release, and λαγως (lagos), a hare, which is an animal with flappy ears that runs loose and hides in holes, and in Greek narratives, symbolizes either the elusive obvious or else the arrogant superior.
Note that in evolutionary terms, humans are apes, which are closely related to their flat-footed and burrow-dwelling brethren the hares, rabbits and mice (whereas cows, sheep, dogs and lions and such form a wholly separate supergroup of heel-lifting surface-dwellers). This not only helps to explain the link between science (the Logos, of Jewish descent) and antiquity's great mystery schools — μυς (mus), means mouse; μουσα (mousa), means muse; μυστηριον (musterion), means mystery — but also why the Jews celebrate their survival of Haman's predatorial holocaust with the feast called Purim, from the noun פור (pur), lot, from the verb פרר (parar), to split or divide.
Our verb λαγχανω (lagchano) to establish by lot or to get by chance, is used 4 times in the New Testament; see full concordance.
The noun λαχανον (lachanon) describes any kind of herb, vegetable or garden plant (any not-wild plant). There is also a verb, λαχαινω (lachaino), which means to dig, not only of holes in the ground to plant herbs in but also iron mines and tombs. A rare but related noun λαχη (lache) means share or allotment and is a synonym (or possibly a variation) of the noun ληξις (lexis), determination by chance (see above).
The verb is probably denominative (derived from the noun) and the origin of the noun is a mystery and deemed probably pre-Greek by the experts. Anything pre-Greek has an excellent chance of being Semitic, and here at Abarim Publications we suspect that our noun may have something to do with the Hebrew root לחח (lahah), which isn't used in the Bible but probably meant to be vigorous and well-watered (as opposed to old and dry). Adjective לח (lah) means moist, fresh or new (Genesis 30:37, Ezekiel 17:24). Noun לח (leah) means freshness or youthful vigor (Deuteronomy 34:7).
Possibly related to this root is the verb לחם (laham), to eat or use as food (hence the name Bethlehem, or House Of Bread), which is identical to לחם (laham), to fight or do battle. Then, of course, there is the noun לחי (lehi), jaw or jaw bone, which is essential for both eating and speaking, and also works wonders when fighting Philistines (means Burrowers). This noun לחי (lehi), jaw, also looks like a compound of ל (le), meaning for, and the noun חי (hay) meaning life: lehayim!
Our noun λαχανον (lachanon), garden plant, is used 4 times in the New Testament; see full concordance.