Etymology
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Words related to lie

*legh- 
Proto-Indo-European root meaning "to lie down, lay."

It forms all or part of: allay; anlage; belay; beleaguer; bylaw; coverlet; fellow; lager; lair; law; lawful; lawless; lawsuit; lawyer; lay (v.) "to cause to lie or rest;" ledge; ledger; lees; lie (v.2) "rest horizontally;" litter; lochia; low (adj.) "not high;" outlaw; scofflaw; stalag; vorlage.

It is the hypothetical source of/evidence for its existence is provided by: 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;" Old English licgan "be situated, have a specific position; remain; be at rest, lie down."
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lain 
past participle of lie (v.2).
lay (v.)

"to cause to lie or rest," Old English lecgan "to place on the ground (or other surface); place in an orderly fashion," also "put down" (often by striking), from Proto-Germanic *lagojanan (source also of Old Saxon leggian, Old Norse leggja, Old Frisian ledza, Middle Dutch legghan, Dutch leggen, Old High German lecken, German legen, Gothic lagjan "to lay, put, place"), from PIE root *legh- "to lie down, lay." This is the causative form of the ancient Germanic verb that became modern English lie (v.2).

Meaning "have sex with" first recorded 1934, in U.S. slang, probably from sense of "bring forth and deposit" (which was in Old English, as in lay an egg, lay a bet, etc.), perhaps reinforced by to lie with, a phrase frequently met in the Bible. To lay for (someone) "await a chance at revenge" is from late 15c.; lay low "stay inconspicuous" is from 1839; to lay (someone) low "defeat" (late 14c.) preserves the secondary Old English sense.

lie-down (n.)
period of rest reclining, 1840, from the verbal phrase (attested from c. 1200); see lie (v.2) + down (adv.).
lier (n.)
"one who reclines; one who is laid to rest," 1590s, agent noun from lie (v.2). Lier-by "kept mistress" is from 1580s.
lying (adj.1)
"being prostrate," late Old English, present-participle adjective from lie (v.2) "to recline."
lying (n.1)
"reclining," early 13c., verbal noun from lie (v.2) "to recline." Lying-in "a being in childbed" is attested from mid-15c.
outlier (n.)

c. 1600, "stone quarried and removed but left unused," from out- + agent noun from lie (v.2). Transferred meaning "outsider" (in reference to persons) is recorded from 1680s, especially "one who does not reside in the place of his office or duties;" the sense of "anything detached from its main body" is from 1849; the geological sense is from 1833.

outlying (adj.)

"outside certain limits, lying beyond the boundary," 1660s, from out- + present participle of lie (v.2). Meaning "remote from the center, lying at a distance from the main body" is attested by 1680s.

outrigger (n.)

"frame device used in the Pacific and Indian oceans to stabilize canoes," 1748, altered (by influence of rig) from outligger (late 15c.) "a spar projecting from a vessel," probably from the same root as Dutch uitlegger, literally "outlier;" see out- + lie (v.2).