Lehman failed because of the 2008 crisis; its failure did not cause or precipitate it. Even Wikipedia lays it out in the opening summary (emphasis mine):

> “A liquidity crisis spread to global institutions by mid-2007 and climaxed with the bankruptcy of Lehman Brothers in September 2008…”

Letting Lehamn fail was the right call, because it allowed the Fed to bulldoze TARP through and save the wider economy as a result. If anything, I would say the subsequent bailouts were too generous in letting the companies retain controls and returns; the government should’ve kept a permanent, partially-nationalized control of those shares and added them to a sovereign wealth fund instead of selling them back on the market. “You fucked up so bad the entire system almost failed, so clearly you cannot be trusted to self-govern” should’ve been the unambiguous messaging from the Fed.