“…the assaults were driven back; and when the Shadow passed, Celeborn came forth and led the host of Lórien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed.” Appendix B, Lord of the Rings.
That last sentence has often puzzled; people wonder exactly how Galadriel might have accomplished such a task. More, why is she doing now what ought to have been accomplished when the White Council drove Sauron from Dol Guldur years before?
The parallels with Luthien’s destruction of Tol-in-Gaurhoth
Conveniently, the tale of Beren and Lúthien offers some guidance: after Lúthien rescues Beren from the captivity of Sauron at Tol-in-Gaurhoth, she puts forth her power to accomplish exactly the same feat.
“Then Lúthien stood upon the bridge, and declared her power: and the spell was loosed that bound stone to stone, and the gates were thrown down, and the walls opened, and the pits laid bare; and many thralls and captives came forth in wonder and dismay, shielding their eyes against the pale moon light, for they had lain long in the darkness of Sauron.” Of Beren and Lúthien, The Silmarillion.
The trick is that in this instance Lúthien’s power derives from the mastery of the tower that she had just wrenched from the defeated Sauron.
Christopher Tolkien confirms as much in his commentary on the Tale of Tinúviel in the second Book of Lost Tales. CJRT draws a clear thread from the Silmarillion version back to the proto-tale which describes how Tinúviel and Huan, the Captain of Dogs, extract from Tevildo the Lord of Cats (a kind of proto-Sauron) the words of magic that bind the stones of Tevildo’s tower together. Tinúviel then uses these words to reduce the fortress to rubble.
CJRT also adds:
“…since my father did not actually say there (in the Silmarillion) that Sauron told Lúthien what the words were, only that he ‘yielded himself’, one may miss the significance of what happened”. The Book of Lost Tales Volume II, The Tale of Tinúviel.
Following this line of logic, I believe it’s not entirely out of the question that in defeating the forces of Dol Guldur, Galadriel compelled a similar mastery from Sauron’s chosen lieutenant. Then, with the secrets of Dol Guldur in hand, she was able to destroy it in a way that the White council was unable to accomplish in TA 2941.