¿Why big banks do not need to lobby the Fed?

Because they own it. So, they are the one that make the decisions. You do not need to lobby your selves.
Yeah, the Federal Reserve Bank of United States is a private entity, and the shareholders are the private banks. They even receive profit (6 percent). Your hear right. The power to decide the interest rates and the money supply in the US is taken by the baking corporations, not by a federal agency.
They call it "cuasi-federal", bullshit. It was created long time ago, in 1913, not by elected politicians, not by independent policymakers, but by a bunch of powerful bankers. The law that created it was conceived in a way that assures that the power to control money stays always in their hands.
Why did the Fed acted in such a irrational way as it did during the Great Depression? Because the people behind it want it a financial crisis to expand the power of the biggest banks such a JP Morgan and others. ¿Why did the Fed abandon the gold standard? Invest taxpayers money to save Bear Stearns, who was a bad financial citizen for a long time in which noboday says nothing, sell it at sale price to JP Morgan, and they tell the people that works in their interesting. Something is missing here..... ¿Want to learn more? Check the documentary: ZEITGEIST EPISODE 3: DON'T MIND THE MEN BEHIND THE CURTAIN in Freedocumentaries.org.