On the evening of Oct. 21, 2014, Carrie Lam sat down with the people. It was the 25th night of the Umbrella Movement, the massive pro-democracy demonstration that would shake Hong Kong for nearly three months, and Lam, a steely bureaucrat who had served as chief secretary, essentially the government’s COO, since 2012, had been sent to represent the government in a televised debate with a delegation of protesters.