Lamb was born in Montclair, New Jersey. He taught himself to play the piano, and was very taken with the early ragtime publications of Scott Joplin. Lamb went to work for a music publisher in New York City where he met his idol Joplin. Joplin was favorably impressed with Lamb's compositions, and reccomended him to a publisher. Lamb, of Irish decent, is usually regarded as the only non African American of the great early classic ragtime composers.
Some of Lamb's best regarded rags include American Beauty, Bohemia, Ragtime Nightingale, Cleopatra, Topliner and Sensation.
When popular music interest shifted from ragtime to jazz at the end of the 1910s, Lamb went to work for an accounting firm, only occasionally playing music as a hobby. With the revival of interest in ragtime in the 1950s Lamb shared his memories of Joplin and other early ragtime figures with music historians, composed some new rags and brought out some of his old compositions that had never been published, and made some recordings.
Lamb died in New York of a heart attack at age 72.