After completing secondary school in 1978 at the Theo-Koch-Schule in Grünberg, Hesse, Lesch studied physics at the University of Giessen, then at the University of Bonn, where he completed his doctoral degree in 1987 and worked at the Max-Planck-Institute for Radio Astronomy. From 1988 to 1991 he was a research assistant at the state observatory at Heidelberg-Königstuhl. In 1992 he was a visiting professor at the University of Toronto. In 1994 he was habilitated at the University of Bonn.
Since 1995 Lesch has been a professor of theoretical astrophysics at the Institute for Astronomy and Astrophysics at the LMU Munich. Additionally, he teaches natural philosophy at the University for Philosophy in Munich. His main areas of research are cosmic plasma physics, black holes, and neutron stars. He is the expert on astrophysics in the Deutsche Forschungsgemeinschaft (DFG) (German Research Society) and a member of the Astronomische Gesellschaft (Astronomical Society). He is also a textbook author.
Lesch has made television appearances for the longstanding, self-presented production of the channel BR-alpha: alpha-Centauri, Lesch & Co., Denker des Abendlandes (Thinkers of the Western World), and Alpha bis Omega (From Alpha to Omega). He also presented shorter television series. His presentations attempt to make complex physical or philosophical issues more accessible to the public. In 2005 he was awarded the Communicator Prize by the DFG and the Stifterverband für die Deutsche Wissenschaft (Foundation for German Scholarship) for his television appearances and publications. To honor his work on making scientific findings understandable to the broad public, the Naturforschende Gesellschaft zu Emden (nature research society) awarded him an honorary membership on March 15, 2011.