ledge (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.

c. 1400, " a book that lies permanently in some specified place" (especially a large copy of a breviary in a church), noun from leggen "to place, lay" (see lay (v.)). Perhaps formed on the model of a Dutch word; the -er seems to indicate "that which has been."

Commercial sense of "book of accounts" is first attested 1580s, short for ledger-book (1550s). Ledger (adj.) "remaining in a place, permanent, stationary" is attested from 1540s; compare ledger-bait "fishing bait made to stay in one place" (1650s).

The surname, however, is via the Normans, from St. Leger, a 7c. bishop whose memory was popular in France and Normandy. The name is Germanic, *Leodegar, literally "people-spear."