After graduating from school in 1923 she entered the Technical University of Hanover to study mathematics and engineering. She obtained her first degree in 1927 and a doctorate in 1929 for a thesis an the mathematical theory of heat.
She then went to the aerodynamics research institute in Göttingen. Here she applied her mathematical skills in solving differential equations to solve an important problem on the distribution of lift on wings. She published what is now known as the 'Lotz method' on 1931.
In 1938 she married Wilhelm Flügge, a civil engineer from Göttingen. In 1944 they moved to a region of Germany which became France at the end of World War II and Flügge-Lotz and her husband both were offered posts at the National Office for Aeronautical Research in Paris.
In 1948 both received offers of posts at Stanford in the United States and accepted. There Flügge-Lotz undertook research in numerical methods to solve boundary layer problems in fluid dynamics. Her pioneering work involved finite difference methods and the use of computers.
Later she worked on automatic control theory and published important works Discontinuous Automatic Control (1953) and Discontinuous and Optimal Control (1958).
Flügge-Lotz became Stanford's first woman Professor of Engineering in 1961. She received many honours including being chosen to give the von Kármán lecture to the American Institute of Aeronautics and Astronautics in 1971 and an honorary degree from the University of Maryland in 1973. The citation read at the ceremony to award the honorary degree states:-
Professor Flügge-Lotz has acted in a central role in the development of the aircraft industry in the Western world. Her contributions have spanned a lifetime during which she demonstrate, in a field dominated by men, the value and quality of a woman's intuitive approach in searching for and discovering solutions to complex engineering problems. Her work manifests unusual personal dedication and native intelligence.