"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.
"uneducated, non-professional; non-clerical," early 14c., from Old French lai "secular, not of the clergy" (12c., Modern French laïque), from Late Latin laicus, from Greek laikos "of the people," from laos "(the common) folk, the people, the crowd; the military; a tribe," in the New Testament especially "the Jewish people," also "the laity," a word of unknown origin. Beekes writes that it is "most often connected with" Hittite lahh- "campaign" and Old Irish laech "warrior," but that the form "is rather Pre-Greek, and has a Pre-Greek suffix -it(o)-. In Middle English, contrasted with learned, a sense revived 1810 in contrast to expert. Laic is a more modern borrowing directly from Late Latin.
"short song," mid-13c., from Old French lai "song, lyric," of unknown origin. Perhaps from Celtic (compare Irish laid "song, poem," Gaelic laoidh "poem, verse, play") because the earliest verses so called were Arthurian ballads, but OED finds this "out of the question" and prefers a theory which traces it to a Germanic source, such as Old High German leich "play, melody, song."
1550s, "act of laying," from lay (v.). From 1580s as "a wager." Meaning "relative position, direction, etc.,; way in which something is laid" (as in lay of the land) first recorded 1819. Slang meaning "line of business" is from 1707. Meaning "woman perceived as available for sex" is attested from 1930, but there are suggestions of it in stage puns from as far back as 1767.