Ben Bernanke just released his memoir which includes his account of the events around the financial crisis. According to Andrew Ross Sorkin, Bernanke claims the decision to not save Lehman in the fall of 2008 was not really a decision. Bernanke claims that the Fed did not have the ability to save Lehman. This is not true. Since the Fed has essentially a limitless ability to lend money, it surely could have provided enough loans at below market interest rates, for a long enough period of time, that Lehman would eventually have been a viable bank.
Sorkin points to $200 billion in losses suffered by Lehman creditors. This is comparable to the sums lent to both AIG and Fannie and Freddie (combined) at the time they faced insolvency, so getting enough money to at least temporarily patch any holes would clearly have been doable. In October of 2008, the assets held by Lehman were near their lowest levels. (That's not based on an analysis of specific assets, just looking at house prices and the price of other assets.)
Suppose that the Fed had lent Lehman the money needed to meet all its immediate obligations and gave the bank Timothy Geithner's "no more Lehmans" guarantee. This was a commitment that big banks would not be allowed to fail. Geithner repeats it endlessly in his autobiography. This would have allowed the bank to continue to operate and presumably make around $3 billion a year in profit (its pre-crisis level) on its ongoing business.
More importantly, the forbearance would have allowed the price of Lehman's assets to recover. In the years since 2008–2009, the stock market has more than doubled. Interest rates on Baa bonds (the lowest investment grade) have fallen by roughly 40 percent, implying a 25–30 percent rise in the price of long-term bonds. Even riskier debt, like many of the assets held by Lehman, has seen an even larger increase in price.
Lehman had roughly $600 billion in assets at the time of its bankruptcy. If its assets rose in value by just 30 percent from that point and it made $20 billion in operating profit over the last seven years, it would be able to fill a $200 billion hole, meaning that it would have been restored to solvency.
Of course, the Fed is not supposed to lend to an insolvent bank under the law, but Citigroup and Bank of America were both almost certainly insolvent in 2008–2010 and they continued to receive support from the Fed. Furthermore, as a practical matter, who was going to stop the Fed from lending to an insolvent bank? Would someone file a lawsuit? It's not clear who would have standing and even if they did, the suit would probably drag on for years before any court tried to interfer with a bailout. At that point it likely would not have been necessary.
So the moral of the story is that the Fed could have rescued Lehman. It could have shoveled huge amounts of money to the bank at below market interest rates and allow Lehman to stay in business even though it was insolvent. At the end of the process, the government could show a profit on the bailout (it would get back more in interest from Lehman than it cost the government to borrow) and then the Washington Post and other news outlets, along with political figures like Timothy Geithner, could boast about how we made a profit on the bailout and laugh at the stupid people who opposed it.