Keep posting your experiences.
I find this situation interesting and will try to look into this a bit more closely. If LR is operating as an exchanger (of paper currencies for their LR liabilities), I'm thinking that there are really not many situations were a "shortage" could be experienced preventing folks from simply exchanging back the way they exchanged in.
Just thinking about it offhand: Either a severe disturbance in the mix of currencies exchanged has taken place (much more XYZ in for LR; concurrently LR out for USD, and similar), or LR is operating on a fractional-reserve basis, and using a portion the demand deposits for other purposes (like any modern bank).
Rothbardians in the forum recognize fractional-reserve as a form of fraud, esp. when not disclosed. So then there is reason to be alert and keep pressing for more detail about this situation.
--edit 201107010007 UTC--
I haven't ever used LR myself, so I'm rather ignorant to the particulars, but in reading their materials I see that LR's organization depends on an independent network of exchangers who are willing to accept LR in exchange for the political or commodity-backed digital currencies they deal in. Apparently the shortage is in LR$ liabilities not USD itself?
So I am trying to mentally playout the transaction process from Mt. Gox.
Say I've got BTC, exchange it at Mt. Gox for LR$ (let's forget Dwolla for the moment). Now I want to move these LR$ off my Mt. Gox account into my own LR account. What has to happen?
And I have to mentally playout the side of the seller(s) which whom I had just traded inside Mt. Gox to get my LR$ balance. Presumably they funded their Mt. Gox accounts with LR$ (forgetting the other methods for the moment).
So for them, they used an indie exchanger to get from fiat-paper money or digital money to LR$, and sent LR$ from their account to Mr. Gox. THEN...Mt. Gox crossed our trade, so I got their LR$ and they got my BTC. So in this case these LR$ exist (they really came to Mt. Gox), so there should be no problem getting Mt. Gox to place them on my LR$ account (they have the funds).
Their could be processing delay. I heard scuttlebutt someplace that Mt. Gox and LR don't yet have a way to fully automate making this transfer. But, in this instance, why the "shortage"? There would be no real shortage (unless Mt. Gox did not keep the LR$ it received from my trading partner in escrow).
Possibly the fact the Mt. Gox is trying to use this amalgamated concept of "dollars" as the trade object against BTC means that they have to horse-about behind the scenes converting the various "dollar" inputs from one service (LR) to another (Dwolla, bank wire of USD, etc.).
How is my logic train here? Could this actually be a Mt. Gox problem, not a problem with the LR organization?