The situation with Lehman Brothers was a mess - first it was allowed to go bankrupt, justified by the Treasury and Federal Reserve as sending a signal that reckless firms couldn't automatically assume any guarantees from the government, but then when the rather obvious fallout of a major inter-linked institution like that going bankrupt caused the markets to freeze up suddenly the official reasoning became that they hadn't had the legal authority to bail them out. That excuse lasted all of a day or two until AIG failed at which point they realised they were staring at financial Armageddon and so a loan of $180 billion was extended. They at least took a major chunk of the company as payment, along with Washington Mutual which they fully seized when it failed, and then Wachovia which they encouraged Citigroup to buy much like with HBOS and Lloyds TSB although Wells Fargo stepped in instead at the last minute. Then all the others that were bailed out.They might not be able to. If I remember correctly the collapse in the banking sector started in America with the collapse of a major American bank that started a cascade reaction in the entire global financial sector.
There's been some speculation since then about whether bailing out Lehman Brothers would have headed the crisis off or at least made it somewhat smaller. Both sides have some compelling arguments, personally I come down of the it wouldn't have stopped things completely but they wouldn't have been as bad side of things. Doing so would have been politically deeply unpopular however.