Thrice shall pay for... what?

[Inziladun]

Another possibility came to mind, prompted by something I remembered Bilbo saying in The Hobbit.

The quote from ROTK that began this thread runs thus:

'Twice you have borne me, Gwaihir my friend,' said Gandalf. 'Thrice shall pay for all, if you're willing.'

When telling the Dwarves he was willing to go back down the tunnel to see if Smaug was gone, Bilbo said:

"'While there's life there's hope!' as my father used to say, and 'Third time pays for all!'"

The 'and' indicates the 'Third time' bit was another of Bungo's sayings. Might Gandalf not have been merely using a little phrase he picked up among those charming and absurd Hobbits, having no particular meaning behind it?