Thrice shall pay for... what?

[Inziladun]

Originally Posted by Pitchwife

From LotR Book VI, The Field of Cormallen, it seems to me that Gwaihir's brother Landroval, rather than Gwaihir himself, was the King of Eagles mentioned in The Hobbit:

That could be the case, but I don't think the quote you cite is conclusive. It could also be read that Landroval and Gwaihir were the 'greatest of all the Eagles of the North'.
Nevertheless, you're probably right about Gwaihir not being the 'king' of the Eagles. Whenever he's mentioned, it always seems to be in the terms of his being the 'swiftest', or having 'far-seeing eyes', and you'd think if he was the ruler of the Eagles that fact would be somewhere noted.