No, Legolas was a Silvan Elf whereas Galadriel was Noldorin. It is possible that Legolas was related to some of the Elves of Lothlorien, but not to Galadriel. All elves are related they all come the same little lake called Cuivienen.
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.
*'To Legolas she sent this word: Legolas Greenleaf long under tree In joy thou hast lived. Beware of the Sea! If thou hearest the cry of the gull on the shore, Thy heart shall then rest in the forest no more.
Legolas does not marry or have any children, based on the appendix of The Lord of the Rings. Regardless of who his mother was, Legolas is the last of his line. When he sails into the West at the beginning of the Fourth Age, he leaves no family members behind.
They are peers, both leaders of different branches of the Elves in Middle-Earth during the Third Age. They have known each other for thousands of years, and given that there is never any mention of them having an uneasy relationship, probably get along fairly well. Otherwise, they have very little relationship.
Why is Galadriel So Powerful | Middle Earth | The Lord of the Rings
Is Legolas Arwen's Brother?
Arwen probably got to know Legolas as her husband's friend and as the leader of the Elven colony in Ithilien. As Mary Tower points out, it is possible that they are distantly related, but it's nowhere stated.
What happened to Gimli and Legolas after Lord of the Rings?
After the War
After the destruction of the One Ring and of Sauron, Legolas stayed for the coronation of Aragorn and his marriage to Arwen. Later, Legolas and Gimli went travelling together to Helm's Deep, visiting the Glittering Caves, and then later traveled through Fangorn Forest as Legolas and Gimli had agreed.
Aragorn and Legolas are long-time companions and best friends since Legolas' father Thranduil sent him to live among the Rangers of the North. Aragorn and Legolas grew close, up to the point where Aragorn revealed his true identity to Legolas. Throughout his journeys, Aragorn and Legolas are as close as brothers.
After the elf offered his bow to Frodo's service (which could barely be considered a whole conversation), the two never spoke again—and though Legolas referred to Frodo in conversation with others, the hobbit never once said the elf's name.
Tauriel truly threw a wrench in Legolas' life when he fell in love with her. She was brave, fierce, and a protective leader of the guard. He was meant to be the dutiful son of King Thranduil, but in loving her, he became a stubborn, masterful archer instead.
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.
The actor is suffering from Legolas Syndrome — where you accidentally get cast into a role that suits you far more than your real-life looks, leaving you with a tricky predicament after the wrap party. Do you A) nick all the costumes and stay in character the rest of your working life, or B)
Legolas came to the Council of Elrond in Rivendell, the great meeting held by the Elf lord Elrond, as a messenger from his father to discuss the escape of Gollum.
Legolas is the son of Thranduil, King of the Woodland Realm of Northern Mirkwood, who appeared as "the Elvenking" in The Hobbit. Thranduil, one of the Sindar or "Grey Elves", ruled over the Silvan Elves or "Wood-elves" of Mirkwood.
Legolas never marries. The closest he gets is spending the rest of his life, as far as we know, with Gimli; they travel around Middle Earth for decades together, and eventually Gimli is given special dispensation to travel to the Undying Lands with his "friend" Legolas—the only dwarf ever to do so.
Their relationship is fraught with awkwardness thanks to Tauriel's solely platonic feelings toward Legolas. Despite the unrequited interest, the two Mirkwood Elves have a great deal of respect for one another and have each other's backs. Legolas also comes to accept that Tauriel does not see him the way he sees her.
Beware of the Sea! If thou hearest the cry of the gull on the shore, Thy heart shall then rest in the forest no more. Lock-bearer, wherever thou goest my thought goes with thee.
Through her great-grandmother, Idril, Arwen was a descendant of King Turgon of the Noldor. Through her mother, she was the granddaughter of the Elf-queen Galadriel of Lothlórien. Through both of her parents, Arwen was a direct descendant of the ancient Elven House of Finwë.
