Litigator David Boies and the law firm he founded, Boies, Schiller & Flexner LLP, have stopped doing legal work for Theranos Inc. after disagreeing about the strategy for handling ongoing government investigations of the blood-testing company, according to people familiar with the matter. Mr. Boies, 75 years old, has been one of the country’s best-known litigators since the late 1990s. He became Theranos’s outside counsel after being approached in 2011 by two investors in the Palo Alto, Calif., startup. He fiercely defended Theranos against questions about its technology and operations. Those efforts included threatening to take legal action against The...