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.