Quote:
I passed over the mountains [Ered Wethrin, then on to Doriath]
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That reading's really a stretch; there's little reason at all to think Galadriel spent any period of time in Hithlum long enough to make "passing over" the Ered Wethrin a significant event in her life. She was after all a Finarfinian, not of Fingolfin's house. In the developed mythos she lived first with her brother in Minas Tirith and Nargothrond, and then in Doriath.
When T wrote that passage it's pretty clear that his idea, at the time, was that Celeborn was a native Silvan Elf and Galadriel had met him in his own land of Lorien, where he had dwelt since the arrival of the Danians/Nandor before the Sun rose. By "mountains" Galadriel could have either meant the Ered Luin or the Hithaeglir; either way doesn't really affect the meaning.* The one really significant bit is the suggestion, never subsequently contradicted, that Galadriel had left Beleriand before the end of the Elder Days.
If one wants to bring in the late writings then the reading fails that way as well, since Galadriel was with Teleporno the whole time since before the Exile.
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*I now really don't recall- I imagine HME covers it- when it was Tolkien decided that Beleriand had been located west of the Shire, that Lindon was its last remnant and the Ered Luin its old eastern fences; was this before or after he wrote the Lorien chapters?