Lepper was born in Canterbury. He studied music at King's College, Cambridge, and went on for specialized studies in piano accompaniment at the Royal Academy of Music, working with Michael Dussek. Lepper won several prizes, including the Gerald Moore Award, for his accompaniment work while a student. He became the BBC Cardiff Singer of the World accompanist in 2003 and has combined that responsibility with an impressive set of collaborations with many of the world's leading singers. These have included mezzo-soprano Dame Felicity Palmer, tenor Mark Padmore, and baritone Benjamin Appl. Lepper has toured Britain, the U.S., and continental Europe with baritone Stéphane Degout, and he made his Carnegie Hall debut with mezzo-soprano Karen Cargill. He has also performed with violinist Carolin Widmann, and the pair earned a Diapason d'Or award in France for their recording of music by Schoenberg, Morton Feldman, Iannis Xenakis, and Bernd Alois Zimmermann, Phantasy of Spring. Another prominent Lepper touring partner has been tenor Ilker Arcayürek, with whom he has presented a Schubert recital in Barcelona, Zürich, and at Wigmore Hall in London. He has performed at the latter with Widmann and with a wide variety of singers, balancing all these recitals with work as a professor of collaborative piano and coordinator of the collaborative piano program at the Royal College of Music in London.
Lepper has been a prolific accompanist to singers on recordings on various labels, and he is equally at home in Romantic repertory and contemporary music. The year 2017 saw Lepper appear on five recordings, all with different singers. In 2019, he returned with Poèmes d'un jour, with Degout, on the B Records label. ~ James Manheim, Rovi