Looby was born April 8, 1899 in Antigua and moved to the United States in 1914. He earned his bachelor’s degree from Howard University in 1922, a law degree from Columbia University School of Law in 1925, and a doctorate in jurisprudence from New York University in 1926.
After graduating, Looby moved to Nashville to take a job as an assistant professor at Fisk University. In 1951, he was elected to the Nashville City Council, one of the first African Americans to be elected since 1911. In 1960, Looby defended the students arrested in the Nashville sit-ins and as a result his house was dynamited.
In 1976, the City of Nashville named a new library and community center in honor of Looby and in 1982 the Nashville Bar Association posthumously awarded him membership, a membership they had denied him in the 1950s.