http://dictionary.reference.com/browse/lay
36. Nautical. to take up a specified position, direction, etc.: "to lay aloft; to lay close to the wind"
...and lots of airplane/airport-related terms are nautical in origin ("cabin", "port" and "starboard", even to "board" a plane).
http://dictionary.reference.com/browse/layover
1870-75, Americanism; noun use of verb phrase lay over