Lumsden was born in Newcastle upon Tyne. He was educated at Dame Allan's School in Newcastle, and Selwyn College, Cambridge, where he was organ scholar from 1948 to 1951. He studied with Boris Ord and Thurston Dart, graduating Bachelor of Arts in 1950 and Bachelor of Music in 1951. In 1951 he married Sheila Daniels; they had two sons and two daughters. After leaving Cambridge, Lumsden held a succession of church appointments. He was assistant organist of St John's College, Cambridge, 1951–53; organist and choirmaster, St Mary's Church, Nottingham, 1954–56; and director of music and rector chori, Southwell Minster, 1956–59. In 1956 he took his PhD, with a dissertation on Elizabethan lute music, a subject on which the Oxford Dictionary of Music ranks him as an authority. Following his church career, Lumsden became fellow and organist of New College, Oxford and lecturer in the faculty of music, University of Oxford 1959–76; Grove's Dictionary of Music and Musicians says of his time there, "He inherited … a choir of high reputation and added to its lustre, as was evidenced by the choir's unusually diverse repertory, its recordings and its impact on audiences during two tours of the USA ". He was director of music at Keele University, 1958–59, and professor of harmony at the Royal Academy of Music, London, 1959–61. As a conductor, Lumsden was founder and conductor of the Nottingham Bach Society, 1954–59, and conducted the Oxford Harmonic Society, 1961–63, the Oxford Sinfonia, 1967–70, and the BBC Scottish Singers, 1977–80. As an organist and harpsichordist he was organist of the Sheldonian Theatre, 1964–76, choragus of Oxford University, 1968–72 and harpsichordist to the London Virtuosi, 1972–75, whose other players were principals of the London Symphony Orchestra. From 1976 to 1982 Lumsden was principal of the Royal Scottish Academy of Music and Drama in Glasgow. He headed the "Save the BBC Scottish Orchestra" action committee in 1980; the BBC abandoned its plan to disband the orchestra. Lumsden was appointed to succeed Sir Anthony Lewis as principal of the RAM from August 1982. He caused controversy in 1988 by what Nicholas Kenyon called "plans to create a high level conservatory … for soloists on the model of the Curtis Institute in Philadelphia", cutting the academy's total number of students. Kenyon added that "the plan caused a huge row with the other music colleges", which felt that this was an attempt to benefit the academy at their expense. Lumsden caused further controversy by bringing in world-famous musicians to "International Chairs" to pass on their knowledge. They included Sir Colin Davis, Lynn Harrell, Hans Werner Henze, Stephen Kovacevich, Anne-Sophie Mutter and Robert Tear. Some members of the RAM faculty felt that occasional visits from star performers added little and even detracted from the day-to-day work of the resident teaching staff. During his time at the RAM Lumsden served as chairman of the National Youth Orchestra and the Early Music Society. He retired from the RAM in 1993.
Lumsden has published two books: An Anthology of English Lute Music, 1954; and Thomas Robinson’s Schoole of Musicke, 1603, 1971. He contributed articles to publications including The Listener; The Score; Music & Letters; the Galpin Society Journal; La Luth et sa Musique; and La Musique de la Renaissance.
