Elvish words beginning with nai- seem to be associated with pain and grief for much of Tolkien’s live. This root first appeared as ᴱ√NAẎA “hurt, grieve” in the Qenya Lexicon, but Tolkien said its original form was probably ᴱ√ŊAH͡YA (QL/65). Under the entry ᴱ√NAẎA it had derivatives like ᴱQ. naike “pain”, ᴱQ. naira “dire, grievous”, and ᴱQ. naitya- “damage, hurt; put to shame, abuse”, but Tolkien linked it to augmented forms like ᴱQ. angayasse “miserable”, which were related to the name of the great chain ᴱQ. Angaino used to bind Melkor (QL/34). In the contemporaneous Gnomish Lexicon the root form was given as ᴱ√ŋaı̯ with derivatives like G. gaist “torment, oppression” and G. gaista- “oppress, cause great grief to” (GL/37).
In The Etymologies of the 1930s, the root form was given as ᴹ√NAY “lament” with a dental nasal rather than a velar (Ety/NAY). Its derivatives had more to do with sadness, such as ᴹQ. naire “lament, sorrow” and N. noer “sad, lamentable”. However, it had what appeared to be an extended form ᴹ√NAYAK “pain” retaining some of its meanings from the 1910s, such as ᴹQ. naike “sharp pain”, though Tolkien did suggested this root might instead be an elaboration ᴹ√NAYKA of the root ᴹ√NAK “bite” (Ety/NÁYAK).
The root reappeared in Definitive Linguistic Notes (DLN) written around 1959 as √NAY “cause bitter grief or pain” with derivatives like Q. naica “bitterly painful or grievous” and Q. naira/S. naer “dreadful, horrible, unendurable” (PE17/151). In this same note Tolkien said √NAY influenced the meaning of √(N)DAY “dreadful, abominable, detestable” in Sindarin; see the entry on √DAY for further details.
This root for “sound” words appeared regularly in Tolkien’s writing, probably to a certain degree contrasted with √LAB which was the basis for Q. lamba “tongue” and Q. lambë “language”. The root √LAM was more specifically for inarticulate vocal sounds and in this sense was the basis for ✶lamā̆n(a) “animal” > Q. laman/S. lavan (WJ/416).
In fact, Tolkien’s earliest use of this root was as the basis for animal words, appearing as unglossed ᴱ√LAMA in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. lama “a head of cattle or sheep; an animal, beast” and ᴱQ. lamáre “flock” (QL/50). In the Early Qenya Grammar of the 1920s, animal words were instead derived from ᴱ✶labna (PE14/70).
The first clear connection of ᴹ√LAM to “sound” was in The Etymologies of the 1930s where it was the basis of words like ᴹQ. láma “ringing sound, echo”, ᴹQ. lamma “sound” and ᴹQ. lámina “echo” (Ety/LAM). In this document, the Noldorin word N. glamor for “echo” was based on the strengthened root ᴹ√GLAM along with words like N. glamm “shouting, confused noise; barbarous speech” (Ety/GLAM); the latter sense survived in words like S. Glamhoth “din-horde” (UT/39), but later Sindarin “echo” word were transferred back to √LAM, as in S. Lammoth “Great Echo” (S/106). In the 1930s and 40s the root was also still connected to animals (PE21/28; PPE22/116).
The root √LAM appeared regularly in Tolkien’s later writings, variously glossed “sound” (VT39/15), “inarticulate voiced sounds” (PE17/138), or “sounds, especially ... vocal sounds, but [it] was applied only to those that were confused or inarticulate” (WJ/416). It remained connected to sound-words (VT39/20), echo-words (PE17/133) and animal-words (WJ/416).