Laurence was born Leib Wolf Siew in Salantai, a small city in the Russian Empire that is now in Lithuania. He emigrated to the United States in 1905, after participating in the Russian Revolution of 1905, and he soon changed his name, taking "William" after William Shakespeare, "Leonard" after Leonardo da Vinci, and "Lawrence" after a street he lived on in Roxbury, Massachusetts (but spelled with a "u" in reference to Friedrich Schiller's Laura). He attended Harvard University (1908–1911; 1914–1915), the University of Besançon (1919) and Harvard Law School (1921) before receiving his LL.B. from the Boston University School of Law in 1925. He became a naturalized US citizen in 1913. During World War I, he served with the US Army Signal Corps.