For most of Tolkien’s life, the Primitive Elvish root for “mother” was √AM. This began with the Qenya Lexicon of the 1910s, where Tolkien gave the root as ᴱ√AMA (QL/30). In The Etymologies of the 1930s it was ᴹ√AM with derivatives ᴹQ. amil and (archaic) N. emil “mother” (Ety/AM¹). In Quenya prayers of the 1950s, the word for mother was Q. Amille. In the last few years of his life, however, Tolkien toyed with the notion of changing this root to √EM. In notes associated with Eldarinwe Leperi are Notessi written in the late 1960s, Tolkien first gave the root as am, but then wrote em next to it with a question mark, along with several new em-derivatives (VT48/19 note #16). The Q. affectionate word emme for “mommy” appeared in the main article, indicating Tolkien did, in fact, adopt this new root, at least for some period of time.
Neo-Eldarin: For purposes of Neo-Quenya writing, I personally prefer to ignore this late change to the root for “mother” and stick with the √AM-forms Tolkien used for most of his life. However, the √AM-forms were less stable in the Sindarin branch of the languages, so I’d use √EM-forms like S. emel and emig, and would assume √AM and √EM were variants of the root, as they were on VT48/19 (see above).
Tolkien used similar roots for “dream” and “sleep” throughout his life, but the exact details varied. In the Qenya Lexicon of the 1910s he gave the root ᴱ√OLO as the basis for the names ᴱQ. Eriol “a dreamer” and ᴱQ. Olofantor who had to do with sleep (QL/69). It had an extended form ᴱ√OLOR with derivatives like ᴱQ. olóre “dream”, but Tolkien indicated these form more properly belonged to the root ᴱ√LORO (QL/69). The entry for ᴱ√LORO had glosses “doze, slumber”, along with derivatives like ᴱQ. lor- “slumber”, ᴱQ. lorda “slumbrous, drowsy”, and ᴱQ. Lôrien “King of Dreams” (QL/56). Various derivatives also appeared in the contemporaneous Gnomish Lexicon such as G. lor- “sleep deep, dream (tr.)”, G. lorc “drowsy, dreamy, lazy”, and G. lûr “slumber” (GL/54, 55), along with G. olma- “dream” and G. oloth “dream, apparition, vision”, probably from ᴱ√OLO³ (GL/62).
In The Etymologies of the 1930s Tolkien first gave the root ᴹ√LOS, revised it to ᴹ√LOR, and then back to ᴹ√LOS (EtyAC/LOS). Tolkien also gave an augmented variant ᴹ√OLOR, which was likewise altered to ᴹ√OLOS (EtyAC/ÓLOS). The unaugmented root was glossed “sleep”, and the augmented root “dream”. The unaugmented root had derivatives like ᴹQ. lóre “slumber” and ᴹQ. lorna “sleep” (Ety/LOS), with Noldorin cognates N. lhûr “slumber” and N. lhorn “asleep” rejected after ᴹ√LOR >> ᴹ√LOS (EtyAC/LOS). The augmented root had derivatives ᴹQ. olor “dream”, N. ôl “dream”, and N. oltha- “to dream” (Ety/ÓLOS). The Quenya form ᴹQ. olor may reflect Tolkien indecision in this period on the development of final -s: compare ᴹQ. kár (kas-) “head” (Ety/KAS). Ultimately he would decide that final -s survived, and intervocalic -s- > -r-, making the derivation of ᴹQ. olor from ᴹ√OLOS somewhat dubious.
In both the 1910s and 1930s, lor- forms were more closely associated with “sleep” and ol- forms with “dreams”. In writings from the 1950s and 60s, the only attested associations for these roots were with “dreams” and “visions”. Tolkien gave √OLOR “vision (of mind)” (PE17/88), olo-s “vision, fantasy” (UT/396) and √OLOS/R “dream” (PM/341). This last mention of the root was from The Shibboleth of Fëanor from the late 1960s, which indicated the root was an extension √OL, but Tolkien continued to use Q. lórë for “dream” in this period (PE17/80; Let/308), and the unaugmented root √LOR was mentioned in passing (without gloss) in a discussion of the root √DOR (PE17/181).
In later writings, Tolkien also used √OLOR or √OLOS as the basis for the true name of Gandalf: Q. Olórin (PE17/88; UT/396). In connection to that name Tolkien wrote:
> olo-s: vision, “phantasy”: Common Elvish name for “construction of the mind” not actually (pre)existing in Eä apart from the construction, but by the Eldar capable of being by Art (Karmë) made visible and sensible. Olos is usually applied to fair constructions having solely an artistic object, i.e. not having the object of deception, or of acquiring power (UT/396).
And also:
> Olor is a word often translated “dream”, but that does not refer to (most) human “dreams”, certainly not the dreams of sleep. To the Eldar it included the vivid contents of their memory, as of their imagination: it referred in fact to clear vision, in the mind, of things not physically present at the body’s situation. But not only to an idea, but to a full clothing of this in particular form and detail (UT/396).
Thus in Tolkien’s later conception, perhaps the most accurate translation of the root would be “(mental) vision”, not properly connected to “sleep” or “(sleeping) dreams” at all. However, the translation of the root as “vision of the mind” seems to have been intertwined with Galdalf’s Quenya name, and remnants of early ideas continued to appear, most especially the long-lived name Q. Lórien “✱Dream Lands” (S/28) as well as S. Lothlórien “Dream Flower” (LotR/467).
Neo-Eldarin: For purposes of Neo-Eldarin, using this root only for “vision of the mind” is problematic, in that it leaves us no good words for “sleep” or “(ordinary) dream”, nor any good explanation for the name (Loth)lórien. I think it is better to hearken back to earlier notions, and assume two distinct roots that influenced each other: √LOR “sleep” and √OLOS “dream, vision”. In Sindarin their derivatives would remain distinct, but in Quenya the two produce similar results, so that Q. lórë came to meaning “dreaming sleep”, usable for either dreams or sleep or both, where Q. olos properly meant “vision of the mind”, but sometimes took the form olor under the influence of √LOR.