A verb meaning “be extended, stretch, be situated (of an area)” appearing in the Quenya Verbal System (QVS) of 1948 based on the root ᴹ√LAT of similar meaning (PE22/126). Tolkien also said that “kaita- to lie is in Q. only used of persons or animals that are lying down (as in bed, asleep or sick). ‘Lie’ said of land or regions is √LAT” (PE22/126).
Conceptual Development: The Qenya Lexicon of the 1910s had ᴱQ. lāta- “spread, extend, lie (of country)” under the early root ᴱ√LAHA (QL/50).
Neo-Quenya: In Tolkien’s later writings caita- was applied to some inanimate things, such as mornië caita “darkness lies” (RGEO/59), so I would assume the statement from QVS given above applies only to flat geographical features like regions or seas. Note that other geographic features either “sit” if short (cities or hills) or “stand” if tall (towers or mountains) (PE22/126), so I would not use caita- to describe any geography.
I would also assume lat- can apply to non-geographical things in the senses “extend, stretch, spread”.
A rejected name for the Númeníoreans from the earliest version of the Fall of Númenor from 1930s (LR/12), a compound of lie “people” and númen “west”.