This Sunday evening, the baritone Laurent Naouri will perform a lost work "written" seven decades ago by the composer Richard Strauss, in honour of a man convicted by the Nuremberg tribunal as a mass murderer and known as the "Butcher of Poland". The performance is the unlikely product of a writing project that traces the parallel lives of three men, culminating at the trial.

The project began with my desire to learn more about the early years of my grandfather Leon, born in Lemberg in 1904. I discovered that the city was once home to two of the most important international lawyers of the 20th century, both of whom were involved in the Nuremberg trials and helped create modern human rights law. Hersch Lauterpacht was a Cambridge academic who had the idea of introducing the term "crimes against humanity" into the Nuremberg statute (and international law) and Raphael Lemkin a Polish lawyer who coined the word "genocide".

The interweaving lives of Lauterpacht and Lemkin – and their connection with the city of Lemberg, which was Lwów in Poland and is now Lviv in Ukraine – led me to a third man. Hans Frank was a German lawyer who worked for the National Socialists from the late 1920s and later served as one of the Nazi regime's principal jurists. In September 1939, Hitler gave him the plum job of governor general of occupied Poland, where he remained until early 1945. Frank caught my attention because of a notorious speech he gave in Lemberg in August 1942, opening the door to mass killings in and around the city. Three years later he was in the dock in Nuremberg.

Though on opposite sides of an ideological divide, Lauterpacht, Lemkin and Frank shared a passion for classical music. This was reflected in their letters and diaries, as well as the conversations they had with others. During those tumultuous years, music offered solace and respite. Lemkin's memoir, written in the 1950s but only published last year, recalled songs sung to him as a small child by his mother, drawn from the poems of Samuel Nadson, a Russian whose words would be set to music by Rachmaninov.

Lauterpacht and Frank had more Germanic tastes, and an appreciation for Johann Sebastian Bach's St Matthew Passion. Lauterpacht, when on the British prosecution team at Nuremberg, wrote of the "moving strains" of the work, suggesting that it offered him strength at a time of acute difficulty. Frank, who sat on the other side of the courtroom, a defendant born Protestant but converted to Catholicism (following his arrest by the Americans, and an unsuccessful suicide attempt), drew strength from the very same piece of music, with its promise of the possibility of mercy. How remarkable that a Jewish prosecutor and a Catholic defendant should be connected by the same piece.

The composer Richard Strauss. Photograph: Corbis

I was surprised to learn that Frank had befriended Strauss (whose daughter-in-law and grandchildren were Jewish). More astonishing yet was the fact that the great composer wrote a piece honouring the Nazi as late as 1943. Strauss walked a tightrope in those years. Soon after the Nazis took power, he was appointed president of the Reichsmusikkammer, the State Music Bureau, composing the Olympische Hymne for the Berlin Olympics. By the time it was performed he had lost the position for insisting that the name of Stefan Zweig – the Jewish librettist of his comic opera Die Schweigsame Frau (The Silent Woman) – should appear at the premiere in Dresden, in 1935.

In 1943, Strauss got into difficulty with the Nazi authorities, and it was Frank who offered support. In thanks, Strauss composed a short piece, the lyrics for which are damningly generous:

Who enters the room, so slender so swank?

Behold our friend, our Minister Frank.

Ever appreciative, Strauss told the writer Klaus Mann, in an interview in 1945 for the US army magazine Stars and Stripes, that Frank was a man who "really appreciated my music". A few weeks later, Frank was in the dock of courtroom 600, in Nuremberg's Palace of Justice, charged with "crimes against humanity" and "genocide".

Struck by what I had learned,, and acutely aware of my musical limitations, I spoke about these musical links to Naouri, a childhood friend. Could the music be woven into a performance that recalled the connection between the three jurists?

Laurent and I collated the elements into an 80-minute performance, of words spoken and sung, with piano accompaniment by Guillaume de Chassy. We wanted to use the piece Strauss wrote for Frank, but learned that the score was "lost". No problem, Laurent said, we can reconstruct the music, "in the style of Richard Strauss". He knew the right person, the French conductor and composer Frédéric Chaslin, living in New York. A few days later the music arrived by email.

Laurent's first rendition of the Strauss/Frank piece must have ended a silence of seven decades. We imagined Frank back at the Wawel Castle, in Krakow, at his piano. The Italian journalist Curzio Malaparte visited Frank there in February 1942, writing about the experience in Corriere della Sera, and later in his novel Kaputt, where he recorded a "conversation" with Frank's wife. "Before taking a crucial decision, or when he is very weary or depressed, sometimes in the very midst of an important meeting," Frau Brigitte Frank says of her husband, "he shuts himself up in this cell, sits before the piano and seeks rest or inspiration from Schumann, Brahms, Chopin or Beethoven."

If such a conversation took place, it did so just a few days after the Wannsee conference at which the Final Solution was agreed. Four years later, Frank was hanged in the courtyard of Nuremberg's Palace of Justice. Strauss died in 1949, at the age of 85.

• The Great Crimes, with Philippe Sands, Laurent Naouri and Guillaume de Chassy will be performed at 8.30pm at the Hay festival on 25 May, at the Southbank Centre, London SE1, on 29 and 30 November and at Stockholm/Interplay on 14 January 2015.