She didn't. She and
Celeborn crossed
Ered Luin before fall of the
Nargothrond.
Oh that's an early version.
Christopher
Tolkien explains in Unfinished
Tales:
"There is no part of the history of
Middle-earth more full of problems than the story of
Galadriel and Celeborn, and it must be admitted that there are severe inconsistencies "embedded in the traditions"; or, to look at the matter from another point of view, that the role and importance of Galadriel only emerged slowly, and that her story underwent continual refashionings.
Thus, at the outset, it is certain that the earlier conception was that Galadriel went east over the
mountains from
Beleriand alone, before the end of the
First Age, and met Celeborn in his own land of
Lórien; this is explicitly stated in unpublished writing [which is now published in History of Lord of the Rings and People of Middle-earth], and the same idea underlies Galadriel's words to
Frodo in The Fellowship of
the Ring II 7, where she says of Celeborn that "He has dwelt in the West since the days of dawn, and I have dwelt with him years uncounted; for ere the fall of Nargothrond or
Gondolin I passed over the mountains, and together through
ages of the world we have fought the long defeat." In all probability Celeborn was in this conception a Nandorin
Elf (that is, one of the Teleri who refused to cross the
Misty Mountains on the Great Journey from
Cuiviénen).
On the other hand, in Appendix B to
The Lord of the Rings appears a later version of the story; for it is stated there that at the beginning of the
Second Age "In
Lindon south of the Lune dwelt for a time Celeborn, kinsman of
Thingol; his wife was Galadriel, greatest of Elven women." And in the notes to The Road Goes Ever On (1968, p. 60) it is said that Galadriel "passed over the Mountains of Eredluin with her husband Celeborn (one of the
Sindar) and went to Eregion." "
Lindon south of the lune is a reference to Harlindon. Harlindon was in
the East of the Ered Luin. Galadriel and Celeborn crossed Ered Luin in early Second Age in all
Sindarin versions of Celeborn.
So yeah, there's a contradiction in the very same book. In LOTR 1 Celeborn was a Nandorin Prince of
Lorien who met with Galadriel when she crossed the mountains of Ered Luin and Misty Mountains in First Age and came to Lorien. In the Appandices to ROTK Celeborn is a Sinda kinsman of Thingol, and he and his wife were living in Harlindon in SA ere they crossed the mountains of Ered Luin.
Also, fun fact, after Tolkien published that Celeborn is a Sinda and soon he wrote his Sindarin origin, he revised a passage about Galadriel's stay in
Doriath. In Later
Quenta Silmarillion 1 Galadriel stayed long in Doriath. But in the revised version, in Later Quenta Silmarillion 2, Tolkien omitted the word "long"! The implication here is that Tolkien had decided that Galadriel stayed in Doriath until the end of it. Originally Galadriel was supposed to stay long, but not until the end, in Doriath. But this was changed in 1958.
Christopher Tolkien is of the opinion that Galadriel aided the Sindar greatly in the Second Kinslaying: "It is a natural assumption that Celeborn and Galadriel were present at the ruin of Doriath (it is said in one place that Celeborn "escaped the sack of Doriath"), and perhaps aided the escape of Elwing to the Havens of Sirion with the Silmaril - but this is nowhere stated."
I wholeheartedly agree with Chris on this.
So it's stated by JRR himself, Celeborn was present in the Ruin of Doriath and escaped. You might question why JRR didn't say Celeborn AND Galadriel escaped the Ruin of Doriath? Well we don't have the full context of that quote. But my guess is that in the context of this quote JRR was focusing on Celeborn, not Galadriel. The same way that in a draft it is stated Galadriel returned to Lorien, and Celeborn's name in this return to Lorien was not mentioned, the draft was more focused on Galadriel. But we know that Celeborn did return to Lorien.
Anyway, assuming Galadriel left her husband and the grandson of her bestfriend goes against her character. It makes her look like a total j*rk. She's "the fairest lady of the
House of Finwë, and the most valiant." She's described as the only woman who is as valiant as the Princes of the
Noldor. She is described as supa wise and supa in love with her mother's kin. She doesn't fear some Feanorians threat against Doriath. She had already fought them in First Kinslaying. In fact, she was ASKING FOR IT. This was her chance to kill Feanorians, as she long had dreamed, especially
Celegorm and
Curufin. In early versions she rejected Eonwë's offer to return to the West only and only because of her love for Celeborn who didn't desire to leave Middle-earth (in later version it was because of her love for all the suffered people). Why would she abandon her great love in Doriath against the threats of Feanorians? In the Fall of Eregion, she fought side-by-side with Celeborn against
Sauron who was at his peak. Why would such a person flee from Doriath when hearing the threat of bunch of
Elves who she is thirsty for their blood? I won't believe that she broke character.
Anyway, Tolkien's son very well knew these and he is very valid on this. His assumption that Celeborn and Galadriel aided in the escape of Elwing is based on a passage where it is generally stated that the survivors of Doriath aided in the escape of Elwing. Galadriel and Celeborn were the closest (known) surviving family of Elwing, and we expect from them to aid their family. Moreover, since they were the most powerful of all survivors they must've been the MVPs. Especially Galadriel who was "the greatest of the Noldor except
Feanor maybe".