This root first appeared as ᴹ√PHILIK “small bird” in The Etymologies of the 1930s with derivatives ᴹQ. filit and N. fileg of the same meaning (Ety/PHILIK). The root also appeared in the contemporaneous Primitive Quendian Structure: Final Consonants with an extra gloss “sparrow”, a deleted variant spilik-, and some additional (unglossed) derivatives ᴹQ. filinke and N. flinc (PE21/56). The root and these last two derivatives reappeared in Common Eldarin: Noun Structure from the early 1950s, in this document with the gloss “finch” (PE21/71-72, 80-81). Note that a likely early precursor to all these words was G. bilinc “sparrow, bird (small)” (GL/23).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to assume the root √PHILIK = “small bird”, with ᴹQ. filit/N. fileg = “sparrow” and Q. filincë/S. flinc = “finch”.
A root connected to singing for all of Tolkien’s life (Ety/GLIR, LIR¹; PE17/27, 67), though its earliest precursor was ᴱ√LIŘI [LIÐI] and thus did not contain the consonant R (QL/54). For further discussion, see √LIN “sing, make a musical sound”.