lie (n.1) Look up lie at Dictionary.com
"an untruth, false statement made with intent to deceive," Old English lyge, lige "lie, falsehood," from Proto-Germanic *lugiz (source also of 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 1909.
In mod. use, the word is normally a violent expression of moral reprobation, which in polite conversation tends to be avoided, the synonyms falsehood and untruth being often substituted as relatively euphemistic. [OED]
lie (n.2) Look up lie at Dictionary.com
"manner of lying, relative position," 1690s, from lie (v.2). Sense in golf is from 1857.
lie (v.2) Look up lie at Dictionary.com
"rest horizontally, be in a recumbent position," early 12c., from Old English licgan (class V strong verb; past tense læg, past participle legen) "be situated, have a specific position; remain; be at rest, lie down," from Proto-Germanic *legjan (source also of Old Norse liggja, Old Saxon liggian, Old Frisian lidzia, Middle Dutch ligghen, Dutch liggen, Old High German ligen, German liegen, Gothic ligan "to lie"), from PIE *legh- "to lie, lay" (source also of Hittite laggari "falls, lies;" Greek lekhesthai "to lie down," legos "bed," lokhos "lying in wait, ambush," alokhos "bedfellow, wife;" 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").

Especially "to lie in bed," hence often with sexual implications, as in lie with "have sexual intercourse" (c. 1300), and compare Old English licgan mid "cohabit with." To lie in "be brought to childbed" is from mid-15c. To lie to at sea is to come to a standstill. To take (something) lying down "receive passively, receive with abject submission" is from 1854.
lie (v.1) Look up lie at Dictionary.com
"speak falsely, tell an untruth for the purpose of misleading," 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 (source also of 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" (source also of Old Church Slavonic lugati, Russian luigatĭ; not found in Latin, Greek, or Sanskrit). Emphatic lie through (one's) teeth is from 1940s.