Denethor had no sons. It may be there is some tenuous connection between the Silvan Elf Celeborn and Lenwë, but Tolkien later decided that Celeborn was to be a Sinda, and very late in his life wanted to make Celeborn into a Falmarin Elf from Aman (a grandson of Olwë). This last conception would have been entirely incompatible with what is published in THE SILMARILLION concerning Galadriel and Celeborn, and possibly the only passage in LOTR where she discusses their history.

What we know of Thranduil (wishes for Mablung connections aside) is that he probably accompanied his father Oropher from Beleriand to the Vales of Anduin. Oropher established a kingdom among the Silvan Elves living in southern Greenwood the Great with his seat on Amon Lanc ("Bald Hill"), later known as Dol Guldur, where Sauron built his early fortress in the Third Age.

Thranduil may have been the son of a Silvan mother, or his parents could both have come from Doriath. However, he probably married a Silvan Elf (which could explain why Legolas thought of himself as a Silvan Elf, unless Tolkien was just using the word "silvan" in the sense of "woodland" -- a view many people hold).

Oropher led the Silvan Elves in the War of the Last Alliance of Elves and Men. He therefore stood as an equal beside Gil-galad and Elendil (and probably Durin IV of Khazad-dum). It was Oropher who initiated the first assault on Mordor prior to Gil-galad's signal. Most of his warriors died with him but the Alliance forced its way into Mordor nonetheless. Thranduil assumed the lordship over his father's people and stayed with the Alliance throughout the rest of the war. He led barely a third of his father's army home in the first year of the Third Age.

Oropher seems to have moved away from Amon Lanc and migrated north through the Greenwood until he settled in the western vales of the Emyn Duir, the Dark Mountains, later known as the Mountains of Mirkwood (from which the Enchanted River of THE HOBBIT flowed). Thranduil dwelt there for about 1000 years until Sauron established Dol Guldur. Then Thranduil led his people north to the Forest River and there establishd his halls (with the aid of Dwarves, Gimli notes in THE TWO TOWERS).

Legolas does not seem to have been alive in the Second Age, so it's possible that -- like Elrond -- Thranduil did not marry until sometime early in the Third Age. It may be that his people lost contact with the Elves of Lorien after he migrated north, or it may be they retained some contact until the rising of the Balrog of Moria, at which time many of Lorien's people fled over Sea and the remnants withdrew into the deeper woods, becoming a secretive and uncommunicative folk.

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Parma Endorion: Essays on Middle-earth, Revised Edition