Well the only Dark Lord of the Sith from the Great Hyperspace War to the Second Great Galactic War was actually the Sith Emperor but during this time there are several "Dark Lords of the Sith" that the Jedi are aware of Freedon Nadd (around 4,350 BBY) was corrupted by Naga Sadow (5,000 BBY); Exar Kun and Ulic Qel-Droma (4,000 BBY) were corrupted by Marka Ragnos (Pre-5,000 BBY), Naga Sadow, and Freedon Nadd. From 3,996-3,959 BBY there was no active Dark Lord as far as the Jedi were concerned. Then after the Mandalorian Wars, Revan and Malak were corrupted by the Sith Emperor. Revan is brainwashed after Malak nearly destroys him. After the death of Malak, Darth Traya and her apprentices Sion and Nihilus come on the scene. Traya is usurped, Sion and Nihilus and ultimately Traya are all defeated and there is another peace for 300 years and that's where the Sith Emperor comes on the scene. I hope that's a decent answer for you.
Does there really need to be one? Even before the whole Sith Emperor stupidity, the KOTOR story was always that Revan (and Malak too, I suppose) reconstituted the Sith, rather than there being a direct continuity (even if some Sith institutions, like the Academy, apparently survived).
That was always my interpretation as well. Adds a bit more import to their decision to become Dark Lords and to the Taris group's fears of the return of the Sith. Though, like you said, the whole Sith Emperor bit changes the narrative.
I'd agree, but we do have semi-active Sith on Korriban after Kun's time. Uln and Sion being two of them. I assume someone is in charge of the Brotherhood after the death of Kun. Much like Dakhan takes over as acting Dark Lord. For the sake of continuity of government, for example. We have Mandalore the Ultimate heading to Korriban, as well, according to Canderous.
I'm not convinced we should be assuming the Brotherhood survives in a meaningful fashion, post-Kun. For all we know it was shattered into a dozen Sith splinter groups, with the Academy being home to but one of them. And, honestly, if Uln was ever recognised as the Dark Lord of the Sith by his students in the pre-Revan days, I'd have expected him to ramble about it. Though there is one instance in KotOR of the position of head master being referred to as "the Dark Lord of Korriban" (should both Uthar and Yuthura be taken care of), so that could have been a title used by Uln at one point. EDIT: For reference-
I always basically just assumed it went the same way as after the Great Hyperspace War, with the remnants splintering and random upstarts anointing themselves the new Dark Lord. Had we actually got to read Mandorla, I was hoping to hear about Dark Lords of loads of planets, with Kun's surviving acolytes all setting up their own personal fiefdoms, Uln's being the faction on Korriban, and someone else naming themselves the Dark Lord of Malachor, another the next Dark Lord of Onderon, or whatever.
I'd like to learn more about said GHW remnants... Not the 'new' ones like the Tribe and Vitiate, but the old ones, like the Sith Sorceress on Ambria, the three Sith at Athiss, and whatever ate three Jedi Masters on Krayiss II.
Yeah, that'd would have been pretty cool. Then you could have had all these titles continuing to exist beneath Revan and Malak's Dark Lord of the Sith. Though maybe informally. "Okay guys, when it's just us, I'm the Dark Lord of Korriban. When Revan and Malak are around, stick to "Head Master", okay?"
Yeah I thought that Jorak Uln, then Uthar Wyyn was just Headmaster of the Sith Academy, like Qorids in Path of Destruction..