In The Etymologies, Tolkien considered a Noldorin variant of this root: ᴹ√GLIN with derivatives ᴹQ. lin-², N. glin- “to sing” and N. glinn¹ “song, poem, lay”. He rejected this variant, however, and its derivatives became ᴹQ. lir-, N. glir- and N. glaer or glîr, all from the root ᴹ√(G)LIR.
After this changes, all of the remaining derivatives of ᴹ√LIN² were actually derived from primitive ᴹ✶lind-; this seems to be the case with derivatives of this root in later writings as well.