This root first appeared in The Etymologies of the 1930s with the gloss “weave” and derivatives like ᴹQ. lanat “weft” and ᴹQ. lanya- “weave” (Ety/LAN). It reappeared in etymological notes from the late 1960s with the gloss “stretch, extend” or “twine” (the latter marked by Tolkien with a “?”), but its two derivatives were Q. lanya/S. lain “thread” (PE17/60).
Neo-Eldarin: For purposes of Neo-Eldarin, I would assume the root remained primarily the basis for weaving words.
A root appearing in Tolkien’s notes on The Rivers and Beacon-hills of Gondor from 1967-69, glossed “rim, edge, border, boundary” and with numerous derivatives of similar meaning (VT42/8). Tolkien coined this root to explain the river name S. Glanduin, which he translated as “Border-river” in this context. In these same notes (or perhaps other notes that were close contemporaries) Tolkien also said the Sindarin name of the Mering Stream in Rohan was S. Glanhír “Boundary Stream” (UT/318).
The Sindarin and Telerin derivatives of this root have an initial gl-, with the sole exception of S. lanc/T. lanca “sharp edge, sudden end”. According to Tolkien: “It is debated whether gl- was an initial group in Common Eldarin or was a Telerin-Sindarin innovation (much extended in Sindarin)”. For the purpose of Neo-Eldarin, I think it is probably best to assume the gl- is from Common Eldarin, to keep this root distinct from √LAN which in earlier writing was the basis for various words having to do with threads and weaving (PE17/60; Ety/LAN).