Mueller was born Elisabeth Neumann in Hamburg. Her father, Fritz C. Neumann, was a teacher at the Oberrealschule im Alstertal [de]. He was a progressive educator and delivered a speech in 1933 to an assembly of Hamburg teachers, warning of the dangers of Nazi ideology. When the Nazis came to power, he was dismissed. Her mother, Ilse (Burmester), an elementary teacher, sustained the family. In 1935, her father was interrogated by the Gestapo for four days. He emigrated, first to Italy, then to the U.S., where he was accepted in 1937 as a political refugee. He became a professor of French and German at Evansville College. She followed with her mother and her younger sister Ingeborg, arriving on 9 June 1939. In the U.S., she used the name Lisel. She graduated from the University of Evansville in 1944. Her mother died in 1953, and she then began to write poetry, publishing the first small collection, Dependencies, in 1965 after twelve years of self-studies.

In 1943, she married Paul Mueller. The couple built a home in rural Lake Forest, Illinois, in the 1960s, and she wrote: “Though my family landed in the Midwest, we lived in urban or suburban environments”. They raised two daughters, Lucy and Jenny. She made money by working as a receptionist in a doctor’s office and writing book reviews for the Chicago Daily News, which hired her in the 1970s.

Mueller’s poems often depart from seemingly simple observations. While her work is in English, it reflects her German roots. She sometimes alludes to German fairy-tales by the Brothers Grimm, and quotes Bertold Brecht. In her 1992 autobiographical poem “Curriculum Vitae”, she writes: “My country was struck by history more deadly than earthquakes or hurricanes”.

Mueller taught at the University of Chicago, Elmhurst College in Illinois, Goddard College in Plainfield, Vermont, and Warren Wilson College. She stopped publishing after her husband died in 2001 and her vision deteriorated.

During her last years, Mueller resided in a retirement community in Chicago, Illinois. She died on February 21, 2020, at the age of 96.