Old English lecgan "to place on the ground (or other surface)," also "put down (often by striking)," from Proto-Germanic *lagjanan (cf. 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"), causative of lie (v.2). As a noun, from 1550s, "act of laying." Meaning "way in which something is laid" (e.g. lay of the land) first recorded 1819.
Meaning "have sex with" first recorded 1934, in U.S. slang, probably from sense of "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. The noun meaning "woman available for sexual intercourse" is attested from 1930, but there are suggestions of it in stage puns from as far back as 1767. To lay for (someone) "await a chance at revenge" is from late 15c.; lay low "stay inconspicuous" is from 1839. To lay (someone) low preserves the secondary Old English sense.
"uneducated; non-clerical," early 14c., from Old French lai "secular, not of the clergy" (Modern French laïque), from Late Latin laicus, from Greek laikos "of the people," from laos "people," of unknown origin. In Middle English, contrasted with learned, a sense revived 1810 for "non-expert."
"short song," mid-13c., from Old French lai "song, lyric," of unknown origin, perhaps from Celtic (cf. 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, cf. Old High German leich "play, melody, song."