During the 2008 financial crisis, almost any of the major Wall Street banks could have gone bankrupt. Lehman Brothers was the unlucky one to be allowed to go bankrupt. The rest were bailed out. Why did the Federal Reserve let Lehman Brothers go bankrupt and not other Wall Street banks? Or is it sheer bad luck for Lehman?
Two words: Moral Hazard.
There is a story that says Tim Geithner "wanted it to hurt," and forced a liquidation at $2 instead of $4/share, specifically in order to send a signal.
This answer depends greatly on who you ask.
Some may say the "fog of war" made it difficult to know whether to bail or not to bail. At one point in the "crises", the prevailing thought could have been to go "all no bail", but then seeing Lehman collapse threw cold water on their resolve to not bail the others.
In the Great Depression there were certain Jewish Banks (Bank of United States) that didn't get the same bail out treatment as others. Perhaps Lehman has similar issues. Lehman Bros was founded by brothers who were Jews in the 19th Centurty (Lehman Bros. Wiki). It is doubtful that the same Jewish connection remained in 2008, and improbable that anti-semitism would still have a role in banking today, but it is worth wondering what other prejudices may have grown from the ashes on 1930s anti-semitism, and if there might be elements making effects today.
Along this line of thought, you will never know the juicy details about Lehman until probably 50 years from now. Historically, banking types and family dynasties are tight about their secrets, or at least they aren't running around to Jerry Springer like hollywood celebrities to tell all the mundane stories about what who was thinking about what, and if they should've eaten their vegetables.
If you want a book that really opened my eyes to this sort of social/psycho-analysis, try "The House of Morgan" by Ron Chernow. Fascinating insight into the good old boys networks and the political dramas, and the mistresses, and the drug use...everything including the technical. Reading this, you may be able to draw your own parallels.
I personally would ask "why did the government bail out all of those banks" rather than "why didn't the government bail out Lehman." And I would look for the same scandalous answers among the people doing the bailing, rather than at the banks.
One thing that is difficult to come by is a thrilling account of the lives of the Federal Reserve Board members especially during the times they served. Everything about them always seems technical, without much emotion.
You should now feel welcome to speculate.
Edit: I have a BS in Economics from the University of Delaware. I also follow this sort of thing with great interest.