This article argues that the Federal Reserve is not a lender of last resort.
The purpose of a lender of last resort is that if some bank can’t obtain funds from another bank it can obtain it from the lender of last resort. However, the Federal Reserve lends on a discretionary basis. This means they aren’t a lender of last resort. The Fed is a plain ol’ lender.
It may be the case that a must-lend rule would create a situation superior to the situation today. Friedman’s critique of the Fed causing the Depression was due to a lack of lending. The 2008 financial crisis involved the Fed selectively lending to AIG but not Lehman.
Because the Fed has discretionary power it is not a true LLR and it also suffers from moral hazard, or an incentive to engage in cronyism. It also suffers a calculation problem as a central agent, creates problems as a monopoly, and other problems exist as well, but those are not related to its supposed role as LLR.
Free banking and free money is the efficient solution, but that is a seperate discussion. Here I just wanted to demonstrate the Fed isn’t a true LLR. Some related links are below: