Lympany was born Mary Johnstone in Cornwall, England; later, on the advice of conductor Basil Cameron, changed her last name to an amended version of her mother's maiden name and gave herself a more glamorous first name.
After studying at London's Royal Academy of Music and appearing at age 13 with the Harrogate Symphony Orchestra, with Cameron conducting, Lympany went to study in Vienna with Mathilde Verne, a pupil of Clara Schumann's, and Tobais Matthay.
She made her London debut in 1935 at Wigmore Hall, and during World War II played in the National Gallery lunch-hour concerts organized by Myra Hess. She became quite popular in those years, playing piano concertos throughout Britain. She became the first pianist to record all of Rachmaninoff's preludes, and gave the British premiere of Khachaturian's concerto.
When the war ended, Lympany made her American debut and went on to tour in Europe, Canada, South America, Australia, and India. In the 1970s, her career hit a low point, but she rebounded and in her 70s made tours of the U.S. and rerecorded all of Chopin's preludes.
In 1981, Lympany created a week-long music festival in Rasigures, France, where she had bought a small sheepfold and vineyard. The festival featured the Manchester Camerata, with whom Lympany often played, and such musicans as singers Victoria de los Angeles and Elizabeth Harwood and pianist C_cile Ousset. The festival continued until 1992.