That was not the option for Lehman or any other financial institution, their problems are not competitiveness, just being the part of the financial system where liquidity and "run on the bank" and dependence on Fed for such liquidity is a fact of life, by design.
Bush tried to spend $15 Billion that Congress had already appropriated for auto industry, so called "green" funds, for development of "green" cars. It was a good solution, "strategery" wise, since this "green" money will be wasted in the future, but Congress didn't go along with the plan because Democrats couldn't get enough Republicans to vote for it to provide cover for them. As it is, they took it from "pot of gold" already in TARP. GM already plans to ask for more in January.