[OE] English has two words lie. The verb ‘recline’ goes back, together with its Germanic relatives (German liegen, Dutch liggen, Swedish ligga. Danish ligge), to a prehistoric base *leg-, a variant of the base *lag- which produced lay. Both come ultimately from Indo-European *legh-, *logh-, whose other English descendants include litter and low. The verb ‘tell untruths’ and its related noun come from a Germanic base *leug-, *loug-, represented also in German lügen, Dutch liegen, Swedish ljuga, and Danish lyve. The second syllable of English warlock comes from the same source.
lie (v.1)"speak falsely, tell an untruth," late 12c., from Old English legan, ligan, earlier leogan "deceive, belie, betray" (class II strong verb; past tense leag, past participle logen), from Proto-Germanic *leugan (cognates: Old Norse ljuga, Danish lyve, Old Frisian liaga, Old Saxon and Old High German liogan, German lügen, Gothic liugan), from PIE root *leugh- "to tell a lie."lie (v.2)"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 *legjan (cognates: 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" (cognates: 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 compare Old English licgan mid "cohabit with." To take (something) lying down "passively, submissively" is from (n.1)"an untruth," Old English lyge "lie, falsehood," from Proto-Germanic *lugiz (cognates: Old Norse lygi, Danish løgn, Old Frisian leyne (fem.), Dutch leugen (fem.), Old High German lugi, German Lüge, Gothic liugn "a lie"), from the root of lie (v.1). To give the lie to "accuse directly of lying" is attested from 1590s. Lie-detector first recorded (n.2)"manner of lying," 1690s, from lie (v.2). Sense in golf is from 1857.