New York prosecutors are poised to file civil fraud charges against Ernst & Young for its alleged role in the collapse of Lehman Brothers, saying the Big Four accounting firm stood by while the investment bank misled investors about its financial health, people familiar with the matter said.

State Attorney General Andrew Cuomo is close to filing the case, which would mark the first time a major accounting firm was targeted for its role in the financial crisis. The suit stems from transactions Lehman allegedly carried out to...