Eowyn Tolkien

The lyrics, written in English by Philippa Boyens and then translated by David Salo, are found in the Annotated Score of the film.
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Nú on théostrum licgeth Théodred se léofa
hæ´letha holdost.
ne sceal hearpan sweg wigend weccean;
ne winfæ´t gylden guma sceal healdan,
ne god hafoc geond sæ´l swingan,
ne se swifta mearh burhstede beatan.
Bealocwealm hafað fréone frecan forth onsended
giedd sculon singan gléomenn sorgiende
on Meduselde thæt he ma no wære
his dryhtne dyrest and maga deorost.
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Éowyn is only heard singing the last four lines of the song, ending with the word Bealo, which in Old English meant "evil" or "harm" The first of those lines ("Bealocwealm hafað...") originates from the epic poem Beowulf, line 2265.

Translation
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Now dear Théodred lies in darkness,
most loyal of fighters.
The sound of the harp shall not wake the warrior;
nor shall the man hold a golden wine-cup,
nor good hawk swing through the hall,
nor the swift horse stamp in the courtyard.
An evil death has set forth the noble warrior
A song shall sing the sorrowing minstrels of Meduseld
That noble cousin, who always held me dear
Now is held in darkness, enclosed.
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Art by me
Middle earth Tolkien fantasy art by
Corinna Springl