He started working at night and sleeping during the moring/early afternoon while he was at university.
He was the type of guy that was so good that he didn't really have to follow the university rules very much. He would get into trouble for not following some stupid requirement, but he was so good that they would just let him get away with it.
Besides quantum electrodynamics, Julian worked on radar at the Rad Lab during World War II, unlike most other top physicists who went to Los Alamos Laboratory to work on the atomic bomb, and he made important contributions there on calculating the best shape of the parts and so on.
He was known for being very formal mathematically and sometimes hard to understand, in stark contrast to Feynman which was much more lose and understandable, especially after Freeman Dyson translated him to the masses.
However, QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) does emphacise that he was actually also very practical in the sense that he always aimed to obtain definite numbers out of his calculations, and that was not only the case for the Lamb shift.