In his introduction to the Lay of Leithian in The Lays of Beleriand, Christopher Tolkien writes:
My father never explained the name Leithian 'Release from Bondage', and we are left to choose, if we will, among various applications that can be seen in the poem. Nor did he leave any comment on the significance - if there is a significance - of the likeness of Leithian to Leithien 'England'. In the tale of Ælfwine of England the Elvish name of England is Lúthien (which was earlier the name of Ælfwine himself, England being Luthany), but at the first occurrence (only) of this name the word Leithian was pencilled above it (II. 330, note 20). In the 'Sketch of the Mythology' England was still Lúthien (and at that time Thingol's daughter was also Lúthien), but this was emended to Leithien, and this is the form in the 1930 version of 'The Silmarillion'. I cannot say (i) what connection if any there was between the two significances of Lúthien, nor (ii) whether Leithien (once Leithian) 'England' is or was related to Leithian 'Release from Bondage'. The only evidence of an etymological nature that I have found is a hasty note, impossible to date, which refers to the stem leth- 'set free', with leithia 'release', and compares Lay of Leithian.
(Lays 188-89)
Did that last principal part--ἐλύθην/elúthēn--catch your eye? Or maybe your ear? Because it sure caught mine 46 years ago. The Silmarillion had come out a year before and I was reading The Lord of the Rings two or three times a year at that point. So the combination of form and meaning-- a standard translation of ἐλύθην/elúthēn would be "I was set free" or "I was released"--fairly leaped off the page at me. All I could think of was Lúthien and the long poem about her and Beren called The Lay of Leithian and that leithian means "release from bondage."* λύω is the verb you use if you are talking about freeing slaves or prisoners.
I asked my Greek teacher about ἐλύθην/elúthēn after class. Her name was Stephanie and she was probably the best teacher I ever had. She was so good at making things clear, at correcting you without making you feel like an idiot, and she so obviously loved teaching Ancient Greek. I know how she felt. It was later my favorite course to teach as well, but I didn't do it anywhere near as well as she did. In any event in 1978 Tolkien was still largely looked down on in academic circles. As I recall, she said she supposed a connection between this verb and the words Lúthien and leithian was possible, but I could also tell she wasn't really keen on having a prolonged discussion about it.
As we worked our way through the truly immense verbal system of Ancient Greek, we learned more and more forms of this and other verbs. When we came to the form λυθεῖεν, once again my eye was caught because this form can be transliterated in several ways, that is, we can change the word letter by letter from the Greek alphabet into our own. The Greek letter upsilon, |υ|, is commonly represented in English with |y|, as in analysis for the Greek ἀνάλυσις -- and yes, that derives ultimately from the same root. But as the English spelling upsilon attests, |υ| is not always represented by |y|. The diphthong |ει| -- pronounced like |ay| in day in Attic Greek (think Plato) or |ee| in Koine Greek (think the Gospels) -- can be transliterated as |ei| or |i|. So λυθεῖεν could be transliterated lytheien, lythien, lutheien, or luthien. As we can see, Lúthien sounds like it could have its origin here.
How should λυθεῖεν be translated? By form it is the third person plural aorist optative passive. The aorist tense often refers to past time, like a simple past, but not necessarily. It can also refer to something that happens suddenly. So, for example, the form ἐδάκρυσε/edakruse can mean "he wept" but is often better taken as "he burst into tears." And what's the optative? It's like the subjunctive, only more so. It doesn't refer to facts but to possibilities, intentions, hopes, and fears, to things that have not yet become real and may never become real. So λυθεῖεν by itself could be translated as a wish: "May they be set free" or "I wish that they be set free." Which of course would be a very significant name for a character like Lúthien, who comes by this name as Tolkien makes her more powerful and able to release or set free from bondage more things and people. As Clare Moore has shown in her article on Lúthien in Mallorn 62 (2021), with each successive version of her tale, Lúthien's power and importance grow.
Tolkien was keen on the sound of words. He specifically cited Ancient Greek as a tongue that gave him "'phonaesthetic' pleasure" (Letters #144 p. 265).** It may have been hard to resist the combination of sound and meaning to be found in Lúthien.
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I hope that the list I've created below helps to clarify the name changes Christopher Tolkien refers to in the quoted passage to start this post. I use > to indicate "becomes" or "changes into"
1. The Tale of Tinúviel in The Book of Lost Tales, vol. II (1917-18)
- The daughter of Thingol and Melian is named Tinúviel, and never called Lúthien.
2. Ælfwine of England in The Book of Lost Tales, vol. II (1917-1918)
- Lúthien = Ælfwine > Ælfwine = Ælfwine
- Luthany*** = England > Lúthien = England ("Leithian" pencilled above 1st use of Lúthien for England)
- The daughter of Thingol and Melian is named Lúthien. Beren, not knowing her name, calls her Tinúviel.
- The daughter of Thingol and Melian is named Lúthien. Beren, not knowing her name, calls her Tinúviel.
4. The Sketch of the Mythology (1926) in The Shaping of Middle-earth.
- Lúthien = Lúthien, daughter of Thingol and Melian
- Lúthien = England > Leithien = England
5. Quenta Noldorinwa (the 1930 Silmarillion) in The Shaping of Middle-earth.
- Lúthien = Lúthien, daughter of Thingol and Melian
- Leithien (Leithian 1x) = England
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*** 'Luthany' seems to come from a poem called "The Mistress of Vision," written by Francis Thompson, a poet of whom Tolkien was quite fond:
The Lady of fair weeping,
At the garden’s core,
Sang a song of sweet and sore
And the after-sleeping;
In the land of Luthany, and the tracts of Elenore.
It's interesting to learn -- thanks to Andrew Higgins's paper, 'O World Invisible We View Thee' The Syncretic Nature of Francis Thompson's Visionary Poems,' which is available here -- that in 1968 George Carter suggested in an unpublished PhD dissertation that Carter suggested that "Thompson constructed 'Luthany' by anglicizing the Ancient Greek aorist passive infinitive of 'luo' – 'luthenai', which means 'to be broken' (Carter 1968, p. 62)."