Lord Browne was CEO of oil giant BP during the Texas City refinery explosion in 2005. And his career ended after having lied to a court about the manner in which he had met his boyfriend. The former senior U.K. government adviser on business, and author of “The Glass Closet,” about being gay in the workplace, shares what he knows about crisis management in his new book, “Connect.” His advice could apply to Volkswagen: a company will recover faster from a PR disaster if it has already built up a reservoir of trust with society and consumers.