Lexer was born in Freiburg, Germany, on 22 May 1867, the son of a Professor of German Languages. By the age of nine, he was already showing talent for art and started a course in modelling, sculpturing and painting with a professional sculptor.

Painting and drawing of plaster figures and muscle men converted him to anatomy, and it was but a short step further to the study of medicine. During his medical studies, he was much impressed by a hand operation which was being performed by Herman Maas, the successor to Ernst von Bergmann in Wurzberg, and from this moment, Lexer decided to become a surgeon.

Lexer wrote his thesis in 1890 in Wurzberg and became an instructor in anatomy in 1891–1892 in Merkel’s anatomical institute in Gottingen. In 1892, he moved to Berlin as a surgical resident in the surgical clinic of Ernst von Bergmann, who was a very good teacher and a successful surgeon, researcher and writer. This second surgical clinic of Berlin (II. Chirurgischen Klinink der Universitat Berlin) had become extremely famous through the work of von Bergmann’s predecessors, as well as the work of von Graefe, Diefferbach and von Langenbeck. In 1902, Lexer was appointed Extraordinary Professor in Surgery at the clinic. During this period, there were continuous clinches with Prof. von Bergmann leading to several clashes between both strong and individual personalities. In 1905, Lexer left Berlin for Konigsberg (now Kaliningrad in Russia). As was often the case in Europe during the latter part of the nineteenth century and the first part of the twentieth century, Lexer’s peripatetic activities read almost like those of a nomad. He was appointed Professor of Surgery in Konigsberg (Kaliningrad) from 1905 to 1910 and held similar positions in Jena from 1911 to 1916, in Freiburg from 1919 to 1928 and in Munich from 1928 to 1936.