[Man of the Old Hope]

Lothíriel, wife of Éomer of Rohan, was the daughter of Imrahil, Prince of Belfalas.

She was not Elvish per se, though the House of Dol Amroth was held to have elven-blood in its line.

In what Christopher Tolkien describes as an early manuscript of the Tale of Years, Tolkien wrote an account of the origin of the Line of Dol Amroth:

"Mithrellas, one of the companions of Nimrodel, is lost in the woods of Belfalas, and is harboured by Imrazôr the Númenórean, who takes her to wife (according to the legends and traditions of Dol Amroth); though after a few years she vanishes, whether to wander in the woods or seek the havens. The son of the union of Mithrellas and Imrazôr received the elven-name of Galador; from him the lords of Dol Amroth traced their descent" (The Peoples of Middle Earth, p. 222.

It may well be that the "legends and traditions" of Dol Amroth were true. Among some of the Elves, at least, it appears that the tradition was assumed to have historical basis:

"At length they came to the Prince Imrahil, and Legolas looked at him and bowed low; for he saw that here indeed was one who had elven-blood in his veins. 'Hail, lord!' he said. 'It is long since the people of Nimrodel left the woodlands of Lórien, and yet still one may see that not all sailed from Amroth's haven west over water.'

'So it is said in the lore of my land,' said the Prince, 'yet never has one of the fair folk been seen there for years beyond count'..." (The Return of the King, pp. 181-2).

I've always admired the character of Prince Imrahil, scion of one of the noblest houses of Gondor in whom ran strong the blood of Mithrellas and of the high Númenóreans.