Dawson graduated from Oberlin College in 1925 and went on to earn an Master of Arts and Doctor of Philosophy from Cornell University.
He served on the faculty of the University of North Dakota and the Case Western Reserve University in Cleveland before joining the Folger Shakespeare Library as a reference librarian in 1932. Dawson served in the United States Navy in World World War World War II From 1946 until his retirement in 1967, he was the curator of books and manuscripts for the Folger. He also taught at Howard University from 1975 to 1977.
From 1984 until May 1994, he volunteered as the rare-book librarian for the Washington National Cathedral.
Dawson married Margaret Williams in 1926. They had two children.
She died in 1957.
He was a member of the Catholic University faculty from 1935 to 1972, lecturing to graduate students until 1967.