Those, of any Elven people, who did not perish through bodily death or depart from Middle-earth across the sea would eventually fade. Fading occurred when their fëar 'consumed' their bodies and the body became merely a memory of the fëa.
Gil-Galad is clear that the spirit of the elves is diminishing, as evidenced by the decaying tree of Lindon. According to him, if the elves don't get their hands on mithril, they will either have to catch an early ship to the Grey Havens or else wither away and die.
By and large elves are seen as long-lived, but can be killed. They are not prolific breeders due to their long lives, so ones that fall in battle, and elves are often seen fighting, reduce the population. In many stories, elves have very much the same foibles as humans, greed, hunger for power, resentment, etc.
In the original Tolkien lore, the Elves were beckoned by the Valar to leave Middle-earth and seek out the Blessed Realm of Valinor. Weary from centuries of battling evil and fearing the inevitable fading, the Elves left the lands of Middle-earth for the future of Men and Dwarves after the destruction of the One Ring.
After Aragorn's death, Legolas made a ship in Ithilien and left Middle-earth to go over the sea. His strong friendship with Gimli prompted Legolas to invite him to accompany him to the Undying Lands; making him the first and only Dwarf to do so. He was never seen again in Middle-earth.
However, The Hobbit ended with Legolas deciding to stay out of the forest and continuing to explore. Legolas eventually reconnected with his people, but he began to diverge from their traditionalist views. He often left the forest. He was making close friendships with other races, even Dwarves.
How do elves lose their immortality in Lord of the Rings?
Any Elves that remain in Middle-earth eventually undergo a process of "fading", in which their immortal spirits overwhelm and "consume" their bodies. This renders their bodily forms invisible to mortal eyes, except to those to whom they wish to manifest themselves.
Elves have the ability to live forever thanks to their immortality. Elves like Elrond, who was over 6000 years old in The Lord of the Rings, are not hard to come by. That being said, Elves who go into battle are aware of the risk to their immortality, willing to risk a long healthy life for the sake of a greater cause.
For The Rings of Power, Númenórian hatred of Elves built over time out of jealously for their immortality. In The Silmarillion, Tolkien outlines the downfall of Númenor as a slow burn that began with the Ban of the Valar, which entailed the first Númenórians agreeing to never sail west toward Valinor.
Are any of the elves who first awoke Cuiviénen still around by the time of LOTR? The oldest elf in LoTR is Círdan the Shipwright, the oldest Elf still remaining in Middle-Earth, who appears at the end of Return of the King to sail to Valinor.
Jus like the Two Trees and the Silmarils, mithril possesses the Light of Valinor, the land where elves can return to live for eternity with the Valar. Mithril is the physical manifestation of the very thing that makes elves ageless and wise.
While the date of Legolas's birth is unknown, he was likely born sometime after his grandfather was killed and his father took over the rule of the Woodland Realm. Like all Elves, Legolas is immortal. Elves do not die by natural causes; however, they can be killed in battle.
At that time, Círdan would abandon the Grey Havens and finally travel the Straight Road himself. On some unknown date, he sailed west aboard the Last Ship with his kinsman Celeborn, but when he did so, he took with him the last living memory of the Elder Days in Middle-earth.
Elves who remained in Middle-earth until the Fourth Age and refused the return to Valinor would fade away completely, meaning their souls consumed their bodies, and these Elves would become detached spirits roaming Middle-earth. In this sense, an Elf is still immortal - just formless.
Galadriel leaves Middle-earth in TA (Third Age) 3021 when she is around 8,000 years old. Given that the events of The Rings of Power take place before the Third Age, she's around 5,000 years old in the show. This is also corroborated by her birth date in Valinor of 1362 in the "Years of the Trees".
Dwarves were long-lived, with a lifespan of some 250 years. They breed slowly, for no more than a third of them are female, and not all marry. Tolkien names only one female, Dís, Thorin's sister. They are still considered children in their 20s, as Thorin was at age 24; and as "striplings" in their 30s.
According to Tolkien, in The Lord of the Rings' history and lore, only the Elves of Middle-earth and the beings called the Ainur, which refers to the Valar and their servants the Maiar, are immortal.
The state of Orcs' lives is unknown. Men, Dwarves, Hobbits, and most other races cannot live forever and thus are subject to aging and natural death; however various members of those races have endured longer extended lifespans beyond usual constraints through multiple means.
Lord of the Rings: Legolas Basically Married Gimli. Legolas and Gimli's relationship is strong in The Lord of the Rings, even though it wasn't explicitly romantic in Tolkien's source material. The members of the Fellowship in The Lord of the Rings forge an unbreakable bond while on their mission to destroy the One Ring ...
It is later mentioned that Tauriel is a talented warrior and was therefore made leader of the Mirkwood border guards. Legolas, the son of Mirkwood's Elven king Thranduil, is indicated to be attracted to her, but as she is a lowly Silvan Elf, she does not believe herself worthy of him.
However, a specific scene in The Lord of the Rings has led fans to theorize that Frodo and Legolas didn't talk, not because of time, but because the hobbit didn't know Legolas' name (and was too embarrassed to ask).
