Lislevand was born in 1961 in Oslo, Norway. He studied music and guitar at the Norway Academy of Music from 1980-1984. Further training came over the next three years at the prestigious Schola Cantorum Basiliensis in Basel, Switzerland, where he studied with American lutenist Hopkinson Smith (who was a co-founder of Hesperion XX) and Eugène Dombois.
Lislevand had begun playing with Hesperion XX by 1987, the year he relocated to Verona and began to study seventeenth century Italian music. Of the many recordings Lislevand made with Hesperion XX, the 1993 Astree-Auvidis CD España: Anthology of Spanish Music was among the more popular and critically acclaimed efforts.
In 1993 Lislevand joined the faculty of the Staatliche Hochschule in Trossingen, Germany, a post he still held in 2007. In the new century, Lislevand has continued to appear regularly both as soloist and as chamber player with his own ensemble. His 2006 CD Nuove Musiche, on ECM Records, has achieved great success, both with critics and the public. Because of its success and Lislevand's growing popularity in the U.S., he was invited to appear on the American broadcast network National Public Radio, where he elaborated eloquently on his still controversial approach toward Baroque music performance. La Mascarade (2016) was his first solo recording for the ECM label.