What happens to an elf in Lord of the Rings who dies twice?

Question

An Elf who dies (whether they are in Valinor or Middle-Earth) goes to the halls of Mandos. After a certain time (to be determined by Mandos, its different for each case) they are returned to life in Valinor. For example, Luthien decided to live a mortal life with Beren upon her release.

But what would happen to an Elf who had been released and was then killed?

Glorfindel (who fought and killed a Balrog in Gondolin) was the only elf released who had ever returned to middle earth (Luthien does not count as stated above), so would his soul leave the circle of the world like a human soul if he was killed again? And what about any other released elf who died over in Valinor, would they go again to the halls of Mandos or not?

I havent been able to find any Tolkien information on this second death.

Answer 1

The fate of the two kindreds is pre-determined, and nothing - short of direct intervention by Eru himself (what may be called "Fate") - can change that. This is quite explicit in the Ainulindale. So, in other words, unless a greater power than the Valar had designs and/or intentions for an individual, there is no reason why a second "death" for an Elf would be any different to a first - i.e. back to the Halls of Mandos, wait for the appropriate time, and then be released.

This is semi-backed-up by one of the later essays in HoME; IIRC Laws and Customs, where it is stated that "death" was an unnatural state for the Eldar and that the Valar were obliged to restore them (save in certain - very extreme - circumstances). A restored Elf is still an Elf and there is no reason why things should be different second time round.

Answer 2

As far as I know, there's only one occasion where Tolkien discusses any difference between the first death and any subsequent deaths. In an essay titled "Laws and Customs Among the Eldar", Tolkien suggests that most Elves who die a second time remain in Mandos and are not re-embodied, but they aren't clear on why:

The Eldar say that more than one re-birth is seldom recorded. But the reasons for this they do not fully know. Maybe, it is so ordered by the will of Eru; while the Re-born (they say) are stronger, having greater mastery of their bodies and being more patient of griefs. But many, doubtless, that have twice died do not wish to return.

^{_{History of Middle-earth X Morgoth's Ring Part 3: "The Later Quenta Silmarillion" Chapter 2: "The Second Phase" Laws and Customs Among the Eldar}}

This paragraph further support's Darth Melkor's (user8719's) answer above: it definitively says that Elves who die for a second time still go to Mandos, and implies that re-birth is a possibility for them, albeit one rarely undertaken.

A more detailed discussion on the fate of Eves who die can be found in the answers¹ to What happened to elves when they died or lost the will to live?

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¹ Disclaimer: one of those answers is mine.