How long can elves go without sleeping?

Question

Elves sleep, not just in The Hobbit, but also in LoTR and in The Silmarillion, but it seems they can go without much longer than, for example, dwarves. When Aragorn, Legolas and Gimli were pursuing the orcs to rescue the kidnapped Merry and Pippin, Gimli had to explain to Legolas why they have to rest:

And yet even I, Dwarf of many journeys, and not the least hardy of my folk, cannot run all the way to Isengard without any pause,’ said Gimli. ‘My heart burns me too, and I would have started sooner; but now I must rest a little to run the better. And if we rest, then the blind night is the time to do so.’

‘I said that it was a hard choice,’ said Aragorn. ‘How shall we end this debate?’

‘You are our guide,’ said Gimli, ‘and you are skilled in the chase. You shall choose.’

‘My heart bids me go on,’ said Legolas. ‘But we must hold together. I will follow your counsel.’~LoTR, The Two Towers

When Aragorn later wakes up Legolas is awake, standing there and complaining how much time they'd lost.

As the chase continues, the others are exhausted, but Legolas is fresh as ever:

For many hours they had marched without rest. They were going slowly now, and Gimli’s back was bent. Stone-hard are the Dwarves in labour or journey, but this endless chase began to tell on him, as all hope failed in his heart. Aragorn walked behind him, grim and silent, stooping now and again to scan some print or mark upon the ground. Only Legolas still stepped as lightly as ever, his feet hardly seeming to press the grass, leaving no footprints as he passed; but in the waybread of the Elves he found all the sustenance that he needed, and he could sleep, if sleep it could be called by Men, resting his mind in the strange paths of Elvish dreams, even as he walked open-eyed in the light of this world.

It seems elves can enter some kind of meditative state and 'rest their minds' while being physically active, that is, they can rest without lying down and sleeping.

And the night before they'd met the riders of Rohan:

The night grew ever colder. Aragorn and Gimli slept fitfully, and whenever they awoke they saw Legolas standing beside them, or walking to and fro, singing softly to himself in his own tongue, and as he sang the white stars opened in the hard black vault above. So the night passed.

So it seems that elves can stay awake for an extended period of time with a bit of meditation without consequences. The question is, how long can they do it without a 'proper' sleep? Can they do it indefinitely? Do they need sleep at all?

Answer 1

We don't know

As far as I can tell, this is the only time Tolkien mentions this peculiar habit of Elves; it's not discussed in any of his drafts of the chapter, and I can find no other occurrences of Elvish "sleep-walking" in Tolkien's texts.

I would, however, submit the possibility that this is just how Elves sleep; later in the same chapter we see Legolas sleeping again, and Tolkien describes it thusly:

Legolas already lay motionless, his fair hands folded upon his breast, his eyes unclosed, blending living night and deep dream, as is the way with Elves.

^{The Two Towers Book III Chapter 2: "The Riders of Rohan"}

What little we know about the relationship between Elves and sleep¹, comes from a 1956 letter, a portion of which was published in A Reader's Companion in their remark on the above quote:

[I]t is plainly suggested that Elves do "sleep", but not in our mode, having a different relation to what we call "dreaming". Nothing very definite is said about it (a) because except at a length destructive of narrative it would be difficult to describe a different mode of consciousness, and (b) for reasons that you so rightly observe: something must be left not fully explained, and only suggested

^{The Lord of the Rings: A Reader's Companion Book 3 Chapter II: "The Riders of Rohan"}

Quite what Tolkien means by this is (intentionally) unclear, but as far as we know this really is just how Elves do.

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¹ Aside from the fact that they do sleep, by numerous example

Answer 2

It seems like this is the regular mode of sleeping for elves

Tolkien's most elaborate comments on elvish sleep habits can be found in the "several pages of roughly written notes" that follow the c.1957 manuscript of "Laws and Customs Among the Eldar".

This note in question was first published in The Nature of Middle-earth.

The occupations of the embodied mind awake are an obstacle to such contacts, lower or higher. They occur therefore, the Eldar say, most often in "sleep" - not in "dreams". But "dreaming" and "sleeping" are to the Elves other than to Men. In sleep the body may, as in Men, cease from all activities (save those essential to life, such as breathing); or it may rest from this or that activity or function¹ as the fëa directs. While it is so, the mind may seek repose also, and be utterly quiet, but it may be absorbed in its own activity: "thinking" - that is, reasoning or remembering, or devising and designing; but these things are at will and of volition. The state that with the Elves nearest resembles human "dreaming" is when the mind is "feigning" or devising.² It is when the mind is quiet and inactive that it most readily receives and perceives contacts from without.

^1. Thus an Elf may stand "asleep" with eyes wakeful, and yet hardly breathe, and with his ears closed to all sound.

^2. Though it is more aware and controlled than in Men, and is usually fully remembered (if the fëa so desires).

_{The Nature of Middle-earth - "Knowledge and Memory"}