In Tolkien’s later writings, caita- was generally used as an intransitive, half-strong verb meaning “to lie (down)”, with a past tense caine (strong) or ceante (half-strong). In Late Notes on Verb Structure (LVS) from 1969, Tolkien provided an alternate conjugation of caita- as a weak verb with past tense caitane (PE22/159), clearly derived from the same root √KAY. This strong conjugation is probably a transitive form of the verb meaning “✱to lay (something down)”.
Conceptual Development: The Qenya Lexicon of the 1910s had ᴱQ. kaita- as a verb meaning “place” under the early root ᴱ√KAYA (QL/46). This early verb hints at another possible meaning for transitive caita-: “to place”. In the Early Qenya Grammar (EQG) of the 1920s, kaita had an intransitive meaning “lie down”, with strong past kaine (PE14/58).
The Quenya verb for “lie” based on the root √KAY of the same meaning (PE17/72; PE22/156). It is a half-strong verb with half-strong past ceantë (PE22/157, 164), but it more commonly uses a strong past caine “lay” (PE17/72; PE22/159; VT48/12) as is often the case for verbs derived from y-roots. This version of the verb is intransitive, but there also seems to be transitive variant caita- “✱lay” with a weak past form caitane (PE22/159); see that entry for discussion.
The verb caita- is not used to describe the location of regions or other flat geographical features like lakes; the verb [ᴹQ.] lat- “spread, extend, be situated” is used for that purpose instead (PE22/126); see that entry for discussion.
Conceptual Development: In the Qenya Lexicon of the 1910s, ᴱQ. kaita- was a transitive verb with the gloss “to place” under the early root ᴱ√KAYA “lie, rest; dwell” (QL/46). The intransitive verbs in this period were ᴱQ. {kaito- >>} kaima- “lie quiet” < ᴱ√KAYA (QL/46) and ᴱQ. kama- “lie down” < ᴱ√KAMA (QL/44). The Early Qenya Grammar of the 1920s had kaita “lie down” (PE14/58), but the first version of the ᴱQ. Oilima Markirya used ᴱQ. kaya- “to lie” (MC/221; PE16/75) and kay- “lie” appeared in Qenya Word-lists from slightly earlier (PE16/132).
Starting in the late 1930s, intransitive “lie” seems to have been only ᴹQ. kaita- (VT27/7; PE22/126).