Lael Brainard's arrival at the White House comes at a critical time for the Fed.

WASHINGTON, Feb 14- In nearly a decade at the Federal Reserve, Lael Brainard advocated for tighter financial regulations, visited underserved communities to explore how U.S. monetary policy affected them and, with subtle twists of discourse, more than once changed the debate over the central bank's stance. A Fed vice chairwoman since last May, Brainard is…