William Lyman Faxon was born around 1837 in Quincy, Massachusetts, to John and Lucy Faxon. His father may have died sometime before 1860. Faxon grew up and attended school in Quincy before enrolling at Harvard University.
He joined the Union army in April 1861, mustering in as an assistant surgeon in the 4th Massachusetts Militia Infantry on April 22, 1861. He mustered out on July 22, 1861. He returned to the Union army in June 1862, becoming an assistant surgeon in the 32nd Massachusetts Infantry. He was promoted to surgeon on August 5, 1863, and he mustered out on June 1, 1865.
He married Annie E. Rundall on October 15, 1863, and they had at least four children: John, born around 1864; Florence, born around 1871; Harold, born around 1874; and Randall, born around 1878. They lived in Chicago, Illinois, and he worked as a doctor. By 1870, he owned $500 of personal property. They returned to Quincy in the 1870s. He applied for a federal pension in January 1895 and eventually secured one. He died of acute indigestion in Wilmington, Massachusetts, on January 19, 1910.