This root and ones like it were connected to “fate” throughout Tolkien’s life. It first appeared as ᴱ√MṚTṚ or ᴱ√M(B)ṚTṚ “chance” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. mart “a piece of luck”, ᴱQ. mart- “it happens” and ᴱQ. marto “fortune, fate, lot” (QL/63). Thus in QL it seems to have more to do with happenstance than destiny, but in the contemporaneous Gnomish Lexicon its derivatives were G. Bridwen “Fate personified”, G. mart(os) “portion, fate, lot”, G. martion “fated, doomed, fey”, and G. umbart or umrod “fate” (GL/24, 56, 75), so perhaps the root meaning had already begun to shift.
In The Etymologies of the 1930s the root appeared as ᴹ√MBARAT “fate” (Ety/MBARAT); this replaced an earlier unstrengthened version ᴹ√MAR-TA, as reflected in the change of the Noldorin form from N. marth >> N. barth (EtyAC/MBARAT), later still N. ammarth >> S. amarth (Ety/MBARAT; SA/amarth). In Notes on Galadriel’s Song (NGS) from the late 1950s or early 1960s Tolkien explicitly said that the root √MAR(AT) or √MBART “doom, fate” was not connected to √MBAR “dwell” (PE17/66), but in notes from the late 1960s he changed his mind and made an etymological connection between the two roots: see √MBAR for details.
This root was connected to the sense “dwell” for all of Tolkien’s life. In the Qenya Lexicon of the 1910s it appeared as ᴱ√MBARA “dwell, live”, though in Qenya it was blended with ᴱ√ŊWAÐA “tarry, linger” since [[eq|initial [ŋʷ] became [m]]] (QL/60). In Gnomish the two roots remained distinct: G. bar “home” (GL/21) vs. G. gwadh- “dwell” (GL/46). However, other Gnomish derivatives hint at an unstrengthened variant ᴱ√MARA: G. mar “Earth, ground, soil” and G. Môr “The Earth”, of which Tolkien said “mar and môr probably conceal two roots and a confusion; mbara” (GL/56). The source of this confusion might be ᴱ√MARA “ripe” (QL/59, 63).
In The Etymologies of the 1930s the root appeared as ᴹ√MBAR “dwell, inhabit” (Ety/MBAR); an earlier version of this entry had the extra gloss “build” (EtyAC/MBAR). In The Etymologies, it seems this root was a strengthened form of ᴹ√BAR “raise” (Ety/BAR), but the root ᴹ√MBARAT “fate” seems to be unrelated at this point (Ety/MBARAT). The root mbar- was mentioned in the Outline of Phonetic Development (OP1) from the 1930s (PE19/36) and again as √MBAR “{house >>} dwell” in the second version of Tengwesta Qenderinwa (TQ2) from around 1950 (PE18/92).
The root √MBAR still had the basic sense “dwell” in Notes on Galadriel’s Song (NGS) from the late 1950s or early 1960s (PE17/64); in those notes it seems it was distinct from both √BAR “raise” and √MAR(AT) or √MBART “doom, fate” (PE17/66). But in notes on Fate from 1968 (NM/226-231; PE17/104-109), Tolkien shifted the meaning of the root:
> English “settle” in its various branches of meaning closely resembles the development of the meanings of √MBAR: thus settlement can mean the act of colonizing or taking up an abode, or the area or place so occupied (by a family or community); or (the terms of) an agreement fixed after debate. The development was not, however, the same: the senses of settle proceed from a sense “place in or take up” a firm position, especially in a place that seems suitable; from which the sense of settling affairs that were in confusion or doubt arose. √MBAR meant basically to make a decision, and the meanings relating to dwelling or occupying land proceeded from that (PE17/105).
This new definition for √MBAR was to support a more direct connection between this root and words like Q. umbar “fate”, hence establishing an etymological relationship to extended √MBARAT for the first time, for example with √MBAR > ✶mbartā- “to define, decree, destine” (PE17/104).
Neo-Eldarin: For purposes of Neo-Eldarin, I think this late 1960s meaning “settle, decide, establish; (by extension) dwell” is probably the best.