Boeing Co’s board of directors failed to challenge then-Chief Executive Dennis Muilenburg on the safety of the 737 MAX or his campaign to counter negative news reports between two fatal crashes that claimed 346 lives, according to freshly released portions of shareholders’ lawsuit that cites internal company documents. Roughly two weeks after the initial crash in late 2018, Mr. Muilenburg devised “a public relations, investor relations and lobbying campaign,” according to the lawsuit, partly designed to push back against the bad publicity and criticism by US airline-pilot groups attacking Boeing’s disclosures regarding the jet’s design. He discussed the plan with then-lead director Kenneth Dubersetein and board member David Calhoun, now Boeing’s CEO, according to internal emails cited in the suit. Around the same time, Boeing was publicly pointing to pilot and maintenance errors as important factors in the catastrophic dive of Lion Air Flight 610 in Indonesia, even as it was privately starting to work on a fix to an automated flight-control system implicated in that crash. The system, called MCAS, later also led to a second MAX crash in early 2019 in Ethiopia.The latest details, contained a recently revised version of a shareholder lawsuit filed in opposition to Boeing’s board in Delaware’s Court of Chancery, included inner workings at the highest levels of the company as it became entangled in one of the largest corporate crises in recent American history. US authorities late last year allowed the MAX to resume passenger flights, ending an almost two-year grounding.