Claudius Lee was born on May 30, 1872 in Culpeper Court House, Virginia. He worked at his father's mill and also served as an apprentice to a gunsmith in Danville. He studied at Lafayette College (Pennsylvania) before being brought to Virginia Agricultural and Mechanical College (now Virginia Polytechnic Institute and State University) to establish the college's physics laboratory while furthering his own education. Graduating with a degree in electrical engineering in 1896, Lee is credited with installing Blacksburg's first telephone switchboard and bringing an electric lighting system to the campus and town. He devised controls to regulate all the college bells and was the university's timekeeper from December 1893 to 1956.

Lee served as superintendent of the campus power plant from 1899 to 1907, and as local manager of the Virginia and Tennessee Telephone Company from 1900 to 1909. He became a professor in 1914. From 1917 to 1919, Lee served in the U. S. Army as a captain of ordnance. Following World War I, he returned to Blacksburg and headed the electrical engineering department from 1919 to 1936. In all, Lee served the college in various capacities for 69 years. The subjects which he taught included telephony, telegraphy, direct and alternating current.

Among the many campus, community and professional organizations in which Lee was involved are the American Institute of Electrical Engineers, the YMCA, Phi Kappa Phi, National Society of Professional Engineers, American Society of Engineering Education, Virginia Academy of Science, Virginia Education Association, Eta Kappa Nu and Tau Beta Pi. He was a trustee of the Blacksburg Methodist Church, in which his wife was also an active member.

Honoring Lee's long service to the university, a residence hall bearing his name was built in the late 1960s. In recent years, however, Lee's campus reputation has been somewhat tarnished by information gleaned from the 1896 Bugle. Within the annual's "organizations" section is a page devoted to the K. K. K., naming Lee as the "father of terror." Lee is also listed as an "arch fiend" in the Pittsylvania Club, whose logo is of the lynching a Black man hanging from a tree. No evidence of campus Klan activity has been found, however, and an investigation has concluded that the pages are racist jokes perpetrated by young men in a nineteenth-century military school dominated by white males. There seems to be no direct evidence in Lee's papers relating to the matter. Several times in recent years, these pages have sparked controversy and led to demands that Lee Hall be re-named. After a petition received over 10,000 signatures in 2020, Lee Hall was renamed Hoge Hall in August of that year.

Lee married Sarah Theresa "Rissie" Otey (born October 14, 1874) on October 24, 1902. their only son, John Henry, died in 1933, the Lees reared Robert and Duval Schultz and Douglas E. Williams. Claudius Lee died December 16, 1962.