His skill in completing Alban Berg’s “Lulu” almost 40 years after Berg’s death was considered one of the greatest operatic achievements of the 20th century.Friedrich Cerha, an Austrian composer and conductor who was best renowned for taking on the arduous task of completing Alban Berg’s unfinished “Lulu,” and whose skill in the effort confirmed that work as one of the greatest operatic achievements of the 20th century, died on Tuesday in Vienna. He was 96.His death was announced by his publisher, Universal Edition. It did not specify a cause.Mr. Cerha wrote several stage works, of which three — “Baal,” “Der Rattenfänger” and “Der Riese vom Steinfeld” — were produced by the Vienna State Opera. He composed orchestral, chamber and other music that found rare stylistic range within the broad confines of postwar modernism. He was a crucial figure in the rebuilding of the Viennese new-music scene, cofounding and then conducting its leading ensemble, Die Reihe. And he was a dedicated teacher to his students, who included the composer Georg Friedrich Haas.But at least outside Austria, Mr. Cerha was known less for his own work than for his celebrated contribution to another composer’s masterpiece.Berg had not quite finished orchestrating “Lulu” when he died in December 1935, although the opera, a successor to his earlier “Wozzeck,” had already become a cause célèbre for critics of Nazi cultural policies. He had set “Lulu” aside earlier that year to write his Violin Concerto and returned to it in the fall only to be struck down, partway into its third act, with an infected abscess.From its Zurich premiere in 1937 on, “Lulu” was staged in a two-act form that offered evidence of the work’s stature yet disfigured the composer’s theatrical and musical design. But by the early 1960s, scholars led by George Perle had become convinced that Berg had considered “Lulu” all but complete, and that the available materials, including a short score, made a realization both possible and necessary. Berg’s widow, Helene, banned any such thing, and his publisher, Universal Edition, publicly followed her lead. Privately, it did not.Mr. Cerha, meanwhile, had long been interested in the Second Viennese School, of which Berg was a part. Mr. Cerha had studied with former members of Arnold Schoenberg’s circle and had programmed a work by Anton Webern for the debut concert of Die Reihe, in March 1959. In June 1962, Mr. Cerha saw Karl Böhm lead “Lulu” at the Theater an der Wien in Vienna and found the two-act truncation painful to watch. The next day, he went to the offices of Universal Edition, asked for whatever documents they had and set secretly to work.A scene from Mr. Cerha’s completed edition of Berg’s “Lulu,” staged by the Paris Opera in 1979. Colette Masson/Roger-Viollet, via Granger The task was considerable. Nine hundred or so bars of one of history’s most complex scores were left to orchestrate, and although Berg’s intricate structure meant that material from the first two acts could be reused in the third, some imagination was still needed. It took Mr. Cerha until 1974 to finish it, before making further revisions after Mrs. Berg died in 1976.There was pressure, too — far more than most composers faced in their own work. “Lulu” already had a towering reputation, and its effective banning by the Nazis had kept it a political symbol after the war. When the Paris Opera finally staged Mr. Cerha’s edition, on Feb. 24, 1979, it offered “perhaps the most important and glamorous operatic premiere since the end of World War II,” Harold C. Schonberg wrote in a front-page review in The New York Times.Mr. Cerha’s contributions were so successful that he became almost a ghostwriter: He revealed “Lulu” at its full greatness, while shying away from the spotlight.His fellow composers were impressed. Pierre Boulez, who conducted the premiere, said Mr. Cerha had worked “with great care, competence and mastery.” Mr. Perle wrote that “nowhere does one have the impression that a hand other than the composer’s has had to take over.”Gyorgy Ligeti went further, saying in 1986 that Mr. Cerha, a friend, had a “total lack of vanity, which enabled him to enter wholeheartedly into the way of thinking of a congenial yet nevertheless different composer, and to sacrifice thousands of hours, and days, of his own composing.”“No one else,” Ligeti added, “could have done that.”Friedrich Paul Cerha was born in Vienna on Feb. 17, 1926, the only child of Paul and Marie (Falbigel) Cerha. His father was an electrical engineer. Friedrich learned the violin from about age 6 and had written a few compositions by the time of Hitler’s annexation of Austria in 1938.Like his parents, young Friedrich despised Nazism, but was conscripted first to aid the Luftwaffe in air defense and later, in 1944, into the Wehrmacht. He deserted, was caught, was sent to the front and deserted again, this time walking hundreds of miles south from Göttingen, in the middle of Germany, through the Thuringian Forest and into the mountains of Tirol, where he hid at high altitude in a hut at Lamsenjoch.The experience of fascism, and of his freedom from it, left Mr. Cerha with a lifelong reluctance to adhere to aesthetic dogmas, or even to focus solely on music; he painted, and sculpted a stone chapel in woods near his second home in Maria Langegg. After studying in Vienna at the conservatory and the university, from which he earned a doctorate in 1950, he spent three summers at Darmstadt, Germany, the hothouse of the European avant-garde, but did not lastingly embrace a single compositional school over another.“I have never fanatically advocated artistic goals,” Mr. Cerha told Universal Edition’s magazine in 2012. “I always acted from an inner conviction.”The legacy of the war is particularly audible in “Spiegel,” a frightening array of seven soundscapes for orchestra and tape that was arguably Mr. Cerha’s most important work. Dating from 1960-61, its clouds of sound resemble the far shorter, more static works that Ligeti wrote around the same time, like “Atmosphères,” and it made Mr. Cerha famous.But “Spiegel,” which he wrote without regard for practicality and did not premiere as a cycle until 1972, is also quite different, with narrative elements that add up to a terrifying hour-plus portrayal of disastrous force. In “Spiegel VI,” a maniacal march slams into nervous strings and winds, the brass braying grotesquely in the ensuing carnage; in “Spiegel V,” relentless drumrolls herald a consuming darkness — the abyss.“The pieces were invented in a purely musical way,” Mr. Cerha wrote in notes for a recording on the Kairos label. “It was only long after their completion that I understood the degree to which this work was influenced by the horrors of my war experiences and the limitless joy of freedom that I felt as a deserter in the midst of nature.”His wife, Gertraud Cerha, a musician herself, whom he married in 1951, was the keyboard soloist in the 1960 premiere of a serialist piece for harpsichord and ensemble, “Relazioni fragili.” She survives him, as do two daughters, Ruth and Irina, and two grandchildren.For some critics, the “Lulu” experience seemed to draw out a Bergian expressivity in Mr. Cerha’s style, and some of his later works — “Nacht” for orchestra, say, or his “8 Sätze nach Hölderlin-Fragmenten” for string sextet — indeed have a familiar, muted lyricism to them, though others do not. He bridled at the suggestion, however: His own works were his, alone.“That was very strange,” he told Universal Edition of this purported influence. “Before the third act of ‘Lulu’ had its world premiere, nobody ever connected me to Berg, but in the years after, this suddenly happened all the time. People detected a connection to Berg, which is of course nonsense.” More