How is Harrenhal administered? That is, does it actually owe fealty to Riverrun, or is it sworn directly to the IT? I know it’s physically in the Riverlands, but it seems like there’s a lot of Iron Throne interference regarding who gets the castle, instead of leaving it to Riverrun (i.e. it seems to always be a reward to a family aligned with the crown; the only other examples I can think of, of the IT just giving a castle outside of the Crownlands to someone, were spoils taken from traitors).

It’s definitely sworn to the Riverlands, but it’s something of a special case because it used to belong to House Hoare until that line was cut off, Aegon the Conqueror has right of conquest over it, and he started a custom by giving it out as a reward to one of his followers, specifically Dragonstone’s master of arms, Quenton Qoherys. (Although he did give the Tullys of Riverrun the Lord Paramouncy and married them into House Qoherys)

House Qoherys ended with the death-by-gelding of Gargon the Guest in 37AC, who had no legitimate issue due to his preference for the First Night. And thus, it reverted back to the Crown. (House Qoherys = total of 37 years)

A few years later, Maegor gave it to Lucas Harroway (who had probably previously been the Lord of Harroway’s Town), who held it only until 44AC when Maegor had all of House Harroway executed for the crime of Alys’ supposed infidelity. (House Harroway = 2-7 years)

He then gave it to House Towers after a melee that killed 23 knights, including Walton Towers. The Towers’ line didn’t last that long, only going for two generations after Walton, and thus it reverted once again. (House Towers = maybe 60 years?)

Jaehaerys gave it to Lyonel Strong, who shared his learning, despite the scandal of his relative Ser Lucamore’s gelding. The Strongs seem to have held Harrenhal for about thirty years (assuming that 30 years = a generation, they would have gotten it around 100 AC), before they died out due to the fire and Cregan Stark. (House Strong = probably 30 years, but could be more, depending on how long the Towers lived)

Harrenhal then reverted to the Crown for about twenty years, when it was given to Lucas “the Pander” Lothston in 151 AC in exchange for marrying Aegon IV’s mistress (and later allowing said mistress and his daughter to have the grossest threesome of all time with Aegon IV in exchange for the Handship). The Lothstons are the longest-running owners of Harrenhal, possibly because they steered into the curse: Lucas survived until at least 178. He was succeeded by Manfryd o’ the Black Hood. (My theory about that name is that Manfryd had a sideline as a “mystery knight” who wore a black hood, and did some really nasty things while in disguise) Manfryd’s heir was (probably his son) Manfred, who betrayed Daemon Blackfyre in 196. He died sometime before 211, when Danelle Lothston took over. 

Danelle seems to have been the last of the line – which may be why the rumors of her sorcery all revolve around Bathory-like attempts to extend her youth and life  – and despite her previous loyalty to the Targaryens, was brought down sometime between 221-233 AC when her black magic became public knowledge. I’m guessing towards the end of that range, given that Ben Blackthumb smithed for Lothstons and is still alive in 299. (House Lothston = ~80 years)

For their part in bringing down Danelle Lothston, the Whents were given Harrenhal by Maekar I, and lasted ~70 years. Might have lasted longer, but Shella’s four sons all died before her, as did her husband. (House Whent = ~70 years) 

And then it reverted to the Crown again, and then was given to the Slynts, who lasted all of three months, and then to the Baelishes. 

Why do you think Harrenhal was left without a lord between the end of the Dance and the Lothstons getting it in 251? From the royal family’s perspective, what could have been done with it?

Between 131 when Larys Strong was executed, and 151 when Lucas “the Pander” Lothston was made Lord of Harrenhal in exchange for marrying Falaena Stokeworth and probably claiming Jeyne as his own daughter, Harrenhal was royal property, just like Summerhall or Dragonstone or King’s Landing. 

Aegon III and his brother Viserys the Hand were probably focused on using Harrenhal’s revenues to help rebuild the royal finances – after all, while Tyland Lannister did send portions of the treasury to Casterly Rock, Oldtown, and the Iron Bank, we never find out what happened to that money and whether the crown got any of that back, and a lot got spent by both the greens and blacks during the war.

The year 131 and after was a bad time – the aftermath of the Dance, an especially hard and long winter, a Winter Fever epidemic, the political dysfunction of the regency, the Red Kraken raiding in the west, etc. When Aegon III took over in 136, his policy of “full bellies and dancing bears” would have required revenue to work, and someone as tight-fisted as Viserys would have looked to the incomes of Harrenhal as a way to make the books balance. 

By 151, there had been 20 years of recovery, and Viserys could afford to give away this royal favor to hush up his son’s indiscretions.