I think you have captured an inconsistency in the Bagehot principle. If the guiding rule is to lend at a penalty rate, then during a liquidity crisis how can the central bank ever fulfill its duty as lender of last resort? The rate that the market requires will rise but the penalty rate will rise even more, such that the central bank effectively prices itself out of the market. After all, if you can transact with the market at x%, why transact at x+1% with the LOLR? Some liquidity provider that is.
At the same time, I'm sure we can all agree that the job of a LOLR is to provide liquidity, not set market prices.
I think the problem here is that we haven't learnt how to properly understand and measure liquidity, and therefore can't price it and provide adequate liquidity insurance policies. Central banks certainly aren't great at it. Because their tools are so blunt, as an unfortunate by-product of acting as LOLR they clumsily prop up asset prices. And that gets everyone angry, and justifiably so.
The best solution would be to devolve the provision of liquidity insurance to the market. Financial products would be developed to provide superior measures of liquidity, and the prices of liquidity for various assets would become public. Taxpayers would no longer have to worry about subsidizing sloppy efforts to provide liquidity to those who may not have paid the market price for the benefits the Fed provided them.Some relevant links:
Liquidity Options by Golts and Kritzman
Liquidity and risk: liquidity as the value of an option to sell at the market price at WWCI (see bob's comments in particular)