The Quenya word for “fall” was Q. lanta- for all of Tolkien’s life, and in his later writings it was derived from the root √DAT, where the [[aq|initial [d] became [l]]] as it usually did in Quenya. But this was not the earliest root for “fall”, which was given as ᴱ√LANTAN in the Qenya Lexicon of the 1910s (QL/51), though the actual primitive form was probably ✱ᴱ√LṆTṆ. This early root is consistent with the Gnomish form G. lantha- “fall onto, settle on, alight” (GL/52). Indeed, this is the most reasonable root in this early period, since [[eq|initial [d] > [t]]] in Early Qenya rather than to [l] as it did later on.
In The Etymologies of the 1930s, however, Tolkien gave the root as ᴹ√DAT “fall down” (Ety/DAT), replacing a deleted root ᴹ√LANTA (Ety/TALÁT; EtyAC/LANTA). Tolkien coined a new Noldorin verb for “to fall”, as N. dant- with passive participle N. dannen “fallen”. The Noldorin verb form dant- was probably archaic or incomplete, and with the proper form most likely matching its later Sindarin form, S. danna- (PE17/62).
The root √DAT “fall” appeared pretty regularly in later notes (VT47/29; VT48/24, 30). In some notes associated with words in The Lord of the Rings, Tolkien gave a new derivation of Q. lanta- and S. danna- from a root DAN-TA (PE17/62), but I suspect this was just the nasal-infixed form of √DAT, as with the similar form ᴹ√DANT from the 1930s (Ety/DAT).
However, in notes from 1968, Tolkien gave √LAT as a variant of √DAT via ancient d/l interchange:
> d and l interchanged frequently in early Common Eldarin, as exemplified by Dat/Lat “fall (to the ground)” (VT47/29).
Detecting this variant in Quenya would be nearly impossible, but it is probably evident in the Sindarin word for “waterfall”: S. lanthir (S/235; PM/349), perhaps < ✱lat-sirē “fall-river”. This variant might be a partial restoration of the early root ᴱ√LṆTṆ, but there are no clear signs of it outside this 1968 note and the Sindarin word for “waterfall”.
The most notable use of the root √(N)DAN “back(wards)” was in the name Q. Nandor for those Elves who joined in the march to Valinor but turned back during the journey (VT48/32); the same root was an element in the earlier name for the Nandor from the 1930s, the Danas (Ety/NDAN). The root first appeared as ᴹ√NDAN “back” in The Etymologies of the 1930s with derivatives like the aforementioned Danas as well as the prefix ᴹQ. nan- “backwards” and the Doriathrin noun dôn “back” (Ety/NDAN). The Etymologies also mentioned an unstrengthened form of the root ᴹ√DAN (Ety/DAN).
The root √(N)DAN appeared several times in Tolkien’s later writings. It appeared among a list of roots having to do with “back” probably composed around 1959 (PE17/166). In this list, Tolkien clarified that in Quenya, √NDAN specifically meant “back” as an action by the same agent revising a previous action, as opposed to an action by a different agent, for which Tolkien coined the root {√TŌ/OTO >>} √KHAN; the example Tolkien gave was Q. nanwen-/S. dadwen- “return, go back [by same agent]” < √NDAN vs. {{Q. tóquet- >>} Q. hanquenta “answer [by a different agent]”. This distinction was lost in Sindarin, however, and √NDAN came to be used for both same and differing agents. Tolkien also said that √NDAN could be used “of return (in same path), retracing, and so employable as un- as in undo”.
The root was mentioned again in the Quendi and Eldar essay from 1959-60, where Tolkien said:
> The name Nandor was a derivative of the element ✱dan, ✱ndan- indicating the reversal of an action, so as to undo or nullify its effect, as in “undo, go back (the same way), unsay, give back (the same gift: not another in return)”. The original word ✱ndandō, therefore, probably only implied “one who goes back on his word or decision”.
Finally, the root appeared in some notes from the late 1960s where √dan- was glossed “retreat, go back, give way (as one advances), revert” serving as the basis for {✶danmi >>} ✶ndanmē > Q. nanwë/S. dannen “ebb-tide”, apparently originally meaning “retreat” (VT48/26 author’s note #2, VT48/32 editor’s note #18). In the same document Tolkien again mentioned the connection of this root to the name of the Nandor.