layup n.

"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.

Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."

As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.

also lay-off, lay off; 1889, "rest, relaxation, respite;" from the verbal phrase; see lay (v.) + off (adv.). Via seasonal labor with periodic inactivity, it came to have a sense of "temporary release from employment," and by 1960s was being used somewhat euphemistically for permanent releases of masses of workers by employers. The verbal phrase lay off is attested from 1841 (colloquial) as "stop working, be idle" (intransitive); 1892 as "dismiss" (an employee); meaning "stop disturbing" is from 1908. Its oldest sense is "remove and lay aside, rid oneself of" (1590s).