Arthur Lyman Williams was born in Oberlin, Ohio, on April 21, 1902 to Lyman Beecher Williams, a carpenter and builder, and Henrietta Wilhelmina (Rick) Williams. He had four brothers, Cranston, Joel ('32), Paul, and Vernon, and a half sister from his father's previous marriage, Fannie Edwards Eichenlaub ('08). Williams attended Oberlin public schools, and in 1925 he received an A.B. from Oberlin College and the S. Mus. B. from the Conservatory. While at student at Oberlin, Williams was a member of several organizations, including the Men's Glee Club, the College Band, and the Conservatory Orchestra, and he directed several of the groups. He studied at Columbia University in 1927, and in 1932-33 he attended the Royal College of Music in London. He received his A.M. from Western Reserve University in 1943.

Williams specialized in school music, and he remained a music teacher for his entire career. His first teaching positions were in the public schools in Howell and Grand Rapids, Michigan, from 1925 to 1928. In 1928, he became Assistant Professor of Wind Instruments at Oberlin College, and he remained with the college until his retirement in 1968. Williams also taught as a Professor of Music Education. As a professor, Williams was described as meticulous and demanding but always willing to help any student in need of assistance. He was concerned with the quality of education at Oberlin and he was active in its preservation. In a 1963 exchange with the newly-chosen Dean of the Conservatory of Music, Norman Lloyd, Williams expressed concern that Lloyd was not supportive of music education in public schools, which would be detrimental to the Music Education program at Oberlin.

From 1928 to 1957, he was Director of Bands at Oberlin, as well as conductor of others ensembles such as the Brass Choir and Symphonic Band. Williams founded the Ohio Intercollegiate Band Festival, billed as the first of its kind anywhere, in 1929. Nearly every summer was spent teaching at music camps or summer sessions, most notably at the National Music Camp in Interlochen, Michigan.

Williams was highly active in professional organizations throughout his career. He served in positions for the Ohio Music Education Association (OMEA), including President; the American Bandmasters Association; and for the College Band Directors Association, among others. Williams was a strong supporter of music education and the nation's bands, and he received numerous citations for his work, such as the Distinguished Service Award by the OMEA in 1955.

In addition to his organization work, Williams was an editor for publications such as the Music Journal magazine and Triad, which he also founded. He had a long list of published articles and books. From articles about woodwind fingering to reporting on activities of state and national organizations, Williams translated his teaching enthusiasm into the written word. Some of the books he edited were The Vested String Choir (1930) with Don Morrison and K.W. Gehrkens, and, also with Gehrkens, The Morrison String System (1934).

Williams was also involved in the Oberlin city community as a deacon at First Church, and as president of the Oberlin City Club, where he took part in parent-teacher work.

In 1932, Williams married Mary Eleanor Maltbie, a 1927 recipient of the S. Mus. B. from Oberlin Conservatory. The couple had one daughter, Carolyn Kelley (Osborn), in 1938, who attended Northwestern University. The Williams family resided in Oberlin almost continuously from 1920, except for the three-year teaching stint in Michigan. On February 22, 1973, Williams passed away in Oberlin; he had been treated in the previous year for Hodgkin's disease.