below – ниже, под, внизу

below (adv.) (из «be» + «low») – дословно – быть низким, снизу.
early 14c., biloogh, from be- "by, about" + logh, lou, lowe "low" (see low (adj.)). Apparently a variant of earlier a-lowe (influenced by other adverbs in be-, cf. before), the parallel form to an-high (now on high). Beneath was the usual word; below was very rare in Middle English and gained currency only in 16c. It is frequent in Shakespeare. As a preposition from 1570s. According to Fowler, below is the opposite of above and concerns difference of level and suggests comparison of independent things. Under is the opposite of over and is concerned with superposition and subjection and suggests some interrelation.

low (adj.) (невысокий; из «lah» - не вырастающий, приземленный; лежащий на земле или в глубоком месте; из протогерманского «lega» из PIE корня *to lie-
"not high," late 13c., from lah (late 12c.), "not rising much, being near the base or ground" (of objects or persons); "lying on the ground or in a deep place" (late 13c.), from Old Norse lagr "low," or a similar Scandinavian source (cf. Swedish låg, Danish lav), from Proto-Germanic *lega- "lying flat, low" (cf. Old Frisian lech, Middle Dutch lage, Dutch laag "low," dialectal German läge "flat"), from PIE *legh- "to lie" (see lie (v.2)).
Meaning "humble in rank" is from c.1200; "undignified" is from 1550s; sense of "dejected, dispirited" is attested from 1737; meaning "coarse, vulgar" is from 1759. In reference to sounds, "not loud," also "having a deep pitch," it is attested from c.1300. Of prices, from c.1400. In geographical usage, low refers to the part of a country near the sea-shore (c.1300; e.g. Low Countries "Holland, Belgium, Luxemburg," 1540s). As an adverb c.1200, from the adjective.

low (n.2) (холм)
"hill," obsolete except in place names, Old English hlaw "hill, mound," especially "barrow," related to hleonian "to lean" (see lean (v.)). Cf. Latin clivus "hill" from the same PIE root.

lie (v.2) (располагаться горизонтально); из староанглийского «licgan» - лежать внизу, отдыхать; из протогерманского «legjanan»
"rest horizontally," early 12c., from Old English licgan (class V strong verb; past tense læg, past participle legen) "be situated, reamin; be at rest, lie down," from Proto-Germanic *legjanan (cf. Old Norse liggja, Old Frisian lidzia, Middle Dutch ligghen, Dutch liggen, Old High German ligen, German liegen, Gothic ligan), from PIE *legh- "to lie, lay" (cf. Hittite laggari "falls, lies," Greek lekhesthai "to lie down," Latin lectus "bed," Old Church Slavonic lego "to lie down," Lithuanian at-lagai "fallow land," Old Irish laigim "I lie down," Irish luighe "couch, grave"). To lie with "have sexual intercourse" is from c.1300, and cf. Old English licgan mid "cohabit with." To take (something) lying down "passively, submissively" is from 1854.

lean (v.) (склоняться, опираться, напр. о стенку); из протогерманского «khlinen»; из PIE корня * klei- склоняться, наклоняться.
c.1200, from Old English hleonian "to bend, recline, lie down, rest," from Proto-Germanic *khlinen (cf. Old Saxon hlinon, Old Frisian lena, Middle Dutch lenen, Dutch leunen, Old High German hlinen, German lehnen "to lean"), from PIE root *klei- "to lean, to incline" (cf. Sanskrit srayati "leans," sritah "leaning;" Old Persian cay "to lean;" Lithuanian slyti "to slope," slieti "to lean;" Latin clinare "to lean, bend," clivus "declivity," inclinare "cause to bend," declinare "bend down, turn aside;" Greek klinein "to cause to slope, slant, incline;" Old Irish cloin "crooked, wrong;" Middle Irish cle, Welsh cledd "left," literally "slanting;" Welsh go-gledd "north," literally "left" -- for similar sense evolution, see Yemen, Benjamin, southpaw).

Интересно, что словарь 1675 этого слова не знает. Равно, как и словарь 1826.
Харпер совершенно зря проводит параллель со словом «lean». Это абсолютно другая корневая группа – «кл» (коло) и её расширение до «клн» Клонить, клониться, наклоняться, колено. Странно, что не приведено в пример слово «клин».
Хотя, как видите, одно из значений слова «low» - Hill (холм).

Нас же интересует корень «- л» и его расширение до «лк» (лж, лг) и пр. То есть в данном случае это корневая группа, развернутая в противоположном направлении от «кл». Лог, лежу (лежать). PIE корень *legh- . На самом деле здесь корень «лг»/ «лж».
Соответственно «below» - это русское «полежу». Замена «п» - «b» и выпадение конечного «ж» (g). В самом деле – «logh» - «lou» - «low». ПЛЖ – PLG – BL.