Size not the only factor
In the case of Bear Stearns, Fannie Mae, and Freddie Mac, company size was just one factor in the government's calculations about whether to throw them a taxpayer-funded lifeline. The nature of their connections with the rest of the economy was far more important.
If Bear Stearns went under, it could have dragged down a web of firms with which it did financial business. Fannie and Freddie together own or guarantee half the nation's mortgages. Their failure could have caused the flow of mortgage money in the US to freeze up.
But if these firms qualify for help, so might Lehman, as well as other financial institutions battered by the housing crisis, such as Washington Mutual, the nation's largest savings and loan.
Lehman is currently bigger than Bear Stearns was before its government-arranged takeover by JP Morgan Chase, after all. Lehman chief Richard Fuld has announced plans to spin off the bank's prized investment management division and split the remainder into two banking entities, one with good loans and one saddled with bad housing-backed assets. If he has time to accomplish this paring, he might reduce the institution's size enough so that US officials might decide it's OK to let it fail, if the situation comes to that.
Lehman does have one advantage that Bear Stearns lacked – access to overnight loans from the Federal Reserve. The Fed initiated this program after the Bear Stearns debacle, so that hard-pressed institutions might be able to stay afloat while they look for cash from other sources.