Lissek initially pursued a law degree at Melbourne University, but his passion for acting led him to abandon his studies halfway through. With a background in amateur dramatics since high school, he refined his craft as a member of the Marlowe Society in the late 1950s.
In 1963, Lissek relocated to Buckinghamshire, England, where he joined Peter Brook's avant-garde Theatre of Cruelty. He made his British screen debut in 1967, playing the role of Lavoisier in Marat/Sade.
Throughout his career, Lissek specialized in portraying offbeat, eccentric characters of diverse ethnicity. He appeared in various television shows, including The Avengers, Special Branch, EastEnders, and Foyle's War, as well as films such as Nicholas and Alexandra, Countess Dracula, and Time Bandits.
In the 1970s, Lissek returned to his birth country, Australia, to play the role of David Garside, a colourful criminal solicitor, in the mini-series Power Without Glory. This led to his casting as Hans Kauffman, a Jewish grocer, in the popular Australian TV soap The Sullivans.
Lissek's extensive theatrical portfolio includes a wide range of roles in Australia, Britain, and the United States, both on and off-Broadway. In 1980, he traveled to Japan for eight weeks to play the role of a Jesuit priest in the acclaimed TV series Shogun, alongside Richard Chamberlain and Toshirô Mifune.
Lissek was married to the English stage and TV actress Heather Canning, who predeceased him in 1996.
