Tolkien used this root for “lie (down)” for most of his life. It appeared as ᴱ√KAYA “lie, rest; dwell” in the Qenya Lexicon of the 1910s (QL/46), but in that document there was another root ᴱ√KAMA “lie down”, with the derivative ᴱQ. kama- “to lie down” (QL/44). There is no sign of ᴱ√KAMA¹ being used this way after the 1910s, and in the 1920s Early Qenya Grammar, the verb for “lie down” was kaita- (PE14/58), which in the Qenya Lexicon of the 1910s had the transitive sense “to place” (QL/44).
The root ᴹ√KAY “lie down” reappeared in The Etymologies of the 1930s (Ety/KAY), and it appeared again in the Quenya Verbal System of the 1940s as the basis for the verb ᴹQ. kaita- “to lie (down)” (PE22/126). The root continued to appear in Tolkien’s later writings all the way up through the late 1960s, always with the sense “lie” (PE17/72; PE22/156).