This root for friendship and devotion first appeared as ᴹ√NIL or strengthened ᴹ√NDIL “friend” in The Etymologies of the 1930s with a number of Quenya derivatives of similar meaning, the most significant being the suffixes ᴹQ. -nil or -dil, which Tolkien said was the equivalent of Old English “-wine” (“-friend”). In The Etymologies, ᴹ√DIL was an unrelated root meaning “stop up, fill up hole” (Ety/DIL). The strengthened root ᴹ√NDIL was mentioned again with the gloss “love, devotion” in The Notion Club Papers of the 1940s (SD/241, 305).
The unstrengthened form √NIL appeared in a letter to David Masson from 1955, where Tolkien said “√NIL means to love as a friend or equal”, as opposed to √(N)DUR which meant “to show special interest in things such as trees, astronomy, gems, medicine, sea, etc.” (PE17/152). Tolkien went on to say that, properly speaking, -(n)dil could apply only to persons and -(n)dur should be used of things, with names like Meneldil and Anardil being “Mannish” misuses of the suffix.
The root appeared again as √(N)DIL “to love, be devoted to” in the draft of a letter to Mr. Rang from 1967, where Tolkien clarified that it described “the attitude of one to a person, thing, course or occupation to which one is devoted for its own sake” (Let/386). This seems to be the only place where Tolkien clearly indicates the unstrengthened form is √DIL. Tolkien again clarified the distinction with √(N)DUR in a footnote:
> This provides the key to a large number of other Elvish Q. names, such as Elendil “Elf-friend” (eled+ndil), Valandil, Mardil the Good Steward (devoted to the House, sc. of the Kings) Meneldil “astronomer” etc. Of similar significance in names is -(n)dur, though properly this means “to serve”, as one serves a legitimate master: cf. Q. arandil “king’s friend, royalist”, beside arandur “king’s servant, minister”. But these often coincide: e.g. Sam’s relation to Frodo can be viewed either as in status -ndur, in spirit -ndil. Compare among the variant names: Eärendur “(professional) mariner” (Let/386).
Neo-Eldarin: For purposes of Neo-Eldarin I would leave the unstrengthened form of this root as √NIL to retain the use of ᴹ√DIL “stop up, fill up hole” from the 1930s. I would also assume that √N(D)IL mainly refers to “devotion”, as opposed to √(N)DUR which mainly refers to “service”. Hence Elendil = “Elf friend” but Valandur = “Servant of the Vala”.
This root was the basis for Elvish “love” words for all of Tolkien’s life. The root first appeared as ᴱ√MELE “love” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. mel- “to love”, ᴱQ. meles(se) “love”, and ᴱQ. melin “dear, beloved” (QL/60). In the contemporaneous Gnomish Lexicon it had similar derivatives like G. mel- “love” and G. melon “dear, beloved” (GL/57).
In The Etymologies of the 1930s Tolkien specified that ᴹ√MEL meant “love (as friend)”, and for the first time it included the derivative N. mellon “friend” (Ety/MEL); Gnomish “friend” words from the 1910s were mostly based on G. ged (GL/38). However, the same entry included ᴹQ. melindo/ᴹQ. melisse “lover” (male and female), so it seems even in the 1930s it could refer to romantic love (Ety/MEL). The root continued to appear in Tolkien’s later writings associated with “love” (PE18/46, 96; PE17/41; VT39/10).
In notes from 1959, Tolkien elaborated on the precise sense of √MEL and its role in romantic and non-romantic love:
> Love, which Men might call “friendship” (but for the greater strength and warmth and permanency with which it was felt by the Quendi) was represented by √mel. This was primarily a motion or inclination of the fëa [“spirit”], and therefore could occur between persons of the same sex or different sexes. It included no sexual or procreative desire, though naturally in Incarnates the difference of sex altered the emotion, since “sex” is held by the Eldar to belong also to the fëa and not solely to the hröa [“body”], and is therefore not wholly included in procreation ... The “desire” for marriage and bodily union was represented by √yer; but this never in the uncorrupted occurred without “love” √mel, nor without the desire for children. This element was therefore seldom used except to describe occasions of its dominance in the process of courting and marriage. The feelings of lovers desiring marriage, and of husband and wife, were usually described by √mel. This “love” remained, of course, permanent after the satisfaction of √yer in the “Time of the Children”; but was strengthened by this satisfaction and the memory of it to a normally unbreakable bond (NM/20).
Thus √MEL was close in sense to Greek “philia”, used of friendship, whereas √YER was used of “eros” or sexual desire. But in Elvish thinking, √MEL was essential for romantic love, and √YER only arose from that. Furthermore, √YER was not the most important element in the love between romantic partners, as the period of procreation and child-rearing took up a relatively small portion of Elvish lives. It was the more enduring feeling of friendship between lovers that really mattered, and thus √MEL was used of both non-romantic and romantic love, though it had not particular sexual connotation.