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.