If you were Aegon the Conqueror, would you have included House Lefford of the Golden Tooth into the Riverlands under House Tully’s Lord Paramouncy or kept them as part of the Westerlands? (P.S. I’m asking Attewell, SLAL and the Good Queen, having huge respect for all y’all’s differing POVs, TY)

Well, it sort of depends on how, as King, you view the loyalty of the Westerlands and the Riverlands. After all, the whole point of Aegon’s Conquest was to assert the unity of Westeros and establish a scenario where wars between kingdoms don’t happen, and given that the only purpose of the Golden Tooth is to ensure that the Westerlands can’t be invaded by the Riverlands but can invade with impunity, the King’s rule should make the Golden Tooth irrelevant. 

So the only scenario where I would see Aegon giving the Golden Tooth to the Riverlands is a scenario in which the new king sees the Riverlands as more loyal than the Westerlands, and needs to forestall any future rebellion which might involve an invasion of the Riverlands. 

Indeed, if it wasn’t for Aegon’s dracocracy leading him to make minimal changes to pre-existing conditions, it wouldn’t be a terrible idea to annex the fortress to the crown to prevent either kingdom from invading the other without openly rebelling.