The failure of Lehman Bros. did not directly cause the financial collapse.

The financial collapse was caused when other banks realized how bad Lehman's balance sheet was. Because their own balance sheets were also bad and they deduced all the other banks out there are probably in just as much trouble.

So banks stopped lending to each other and that's what caused the collapse.

But those circumstances wouldn't have changed if we bailed out Lehman. Because the realization would still have been the same.