Counterpart to the root √N(D)IL, this root first appeared in a marginal note from The Etymologies of the 1930s as ᴹ√NDUR or ᴹ√DUR “bow down, bend (down), obey, serve”, an elaboration of ᴹ√NDŪ “go down, sink, set (of Sun)” (Ety/NDŪ; EtyAC/NDŪ). In the Quenya Verbal System of the 1940s, ᴹ√NDUR was glossed “grow, be dark”, no doubt in connection to N./S. dûr “dark” (PE22/103), but later this “dark” word was connected more directly to √NDU “under, down”. Indeed, in a 1955 letter to David Masson, Tolkien gave √(N)DUR an origin distinct from √N(D)U, basing it on an independent root √DUR “to show special interest in things” (PE17/152); there was also an unglossed and deleted root ᴹ√DUR in The Etymologies of the 1930s (EtyAC/DUR). However, in a 1967 letter to Mr. Rang, -(n)dur again meant “to serve” (Let/386).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to keep the connection between √NDUR “bow down = serve” and √NDU “descend”. As for the semantic distinctions between -(n)dil and -(n)dur, see the entry on the root √N(D)IL for details.
A root variously glossed as “flow (strongly)” or “flood, drench, inundate”, its most notable derivative is S. duin “(large) river”, which is an element in many river names such as S. Anduin or S. Baranduin. Its first precursor seems to be primitive ᴱ√*dui** mentioned in Gnomish Lexicon of the 1910s as the basis for words like G. duif “stream” but also G. duil* “flight” (GL/31, 45), so perhaps meaning “flow” in both water and air.
It appeared in The Etymologies of the 1930s as ᴹ√DUI̯, mostly with Ilkorin derivatives though Tolkien noted it was also used in Noldorin (Ety/DUI; EtyAC/DUI). The root dui- appeared again in Tolkien’s 1967 notes on the Nomenclature of the Lord of the Rings, again as the basis for S. duin; in these notes he specified that its Quenya equivalent Q. luine was not used (RC/766).
Tolkien mentioned this root again in some 1968 etymological notes, where he said that other Quenya derivatives like Q. luimë “flood” and luita- “to flood” did survive (VT48/23). When Tolkien first wrote this note, he considered but rejected having a Q. form nuine “river” (VT48/30), perhaps by assimilation of the initial d- to the following n. Despite the repeated rejection of the Quenya cognate of S. duin, it does appear in a couple Quenya river names, such as Q. Anduinë and Nunduinë, so perhaps it survived in compounds as suggested by Patrick Wynne (VT48/30-31, note #6) or was restored as a late borrowing from Sindarin.