Here is the Treasury's Assistant Secretary for Economic Policy on why the Fed bailed out plenty of other institutions, but did not bail out Lehman:

The reluctance of the Federal Reserve to lend to Lehman contrasts with its actions regarding Bear Stearns and A.I.G. The difference is that in the other two cases, the Fed saw itself as lending against reasonable collateral.

In the case of the Fed’s loans that facilitated the acquisition of Bear Stearns by JPMorgan Chase, $29 billion of Fed money was at risk against a collection of Bear Stearns assets thought to be worth $30 billion. JPMorgan would absorb the first $1 billion if the value of those assets declined, providing a cushion ahead of the Fed (that is, ahead of taxpayers). Those assets were good in the end, with the Fed fully repaid with interest.

In the case of A.I.G., the Fed’s loans were collateralized by the entire assets of the firm, based on the observation that A.I.G. had potentially huge losses at its unit that sold credit default swaps but the rest of the firm was a successful insurer. The latter parts — the rest of the company — provided the collateral for the Fed’s initial loans, and eventually TARP funds were substituted for the Fed resources to provide the company with a better capital base rather than Fed loans. To be sure, it was hard to know in September 2008 that the value of the company would offset the potential losses in A.I.G.’s financial products division, but this turned out to be the case, with both the Treasury and the Fed turning considerable profits on their investments in A.I.G.

Such a successful outcome was simply less imaginable with Lehman than with either Bear Stearns or A.I.G. To all eyes, the problem at Lehman was one of solvency while the issue in the other two cases was liquidity. The Fed’s actions on Bear and A.I.G. were thus appropriate in its role as a lender of last resort and the same with its caution at Lehman. Indeed, after Lehman had filed for bankruptcy, the Fed did extend loans to allow the firm’s broker-deal subsidiary to function, but in bankruptcy these loans could be fully collateralized by assets within the brokerage subsidiary and not encumbered by obligations in other parts of the larger firm. [1]

Basically, Bernanke knew that Lehman owned a bunch of worthless paper whereas firms like AIG, GM, Fannie Mae + Freddie Mac, Goldman, etc. owned actual valuable assets that they could use as collateral against taxpayer loans, and operated in profitable segments outside of risky IB and junk-debt securitization. He was tight-lipped about saving Lehman Bro's because he wanted the private sector to step up and do it themselves, and also so that they wouldn't know whether or not to expect handouts from the Fed down the road.

Although I disagree with Bernanke's decision to adhere to Keynesian economics during the economic crisis, valuing short-term stability over properly setting precedents for long-term prosperity and growth, I have to respect the man for his intelligence and thoughtfulness. Looking forward to reading his account of the crisis and why he made the decisions that created the economic environment as it currently stands.

[1] http://economix.blogs.nytimes.com/2013/09/13/why-lehman-wasn...