A root appearing in Late Notes on Verb Structure (LVS) from 1969 as √NAYA “have opportunity, chance or permission; be allowed by circumstance [or] way of the world” giving a new etymology for Q. nai “it may be”.
Neo-Eldarin: For purposes of Neo-Eldarin, I would ignore this root since it conflicts with the much better established √NAY “grief, pain”, and would stick with the well established etymology of Q. nai “maybe, be it that” = Q. ná- + Q. i.
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.