Lenz was born to a Prussian and devoutly Lutheran notary in Greifswald, Province of Pomerania. After graduating from school, he studied history and classical philology under Heinrich von Sybel for three semesters in Bonn. He served in the 1870-1871 Franco-Prussian War and was wounded in the Battle of Villiers. He then continued his studies, at first in Greifswald for one semester, and then in Berlin.