John Linzy Fish was born on March 2, 1839, in Chelmsford, Massachusetts, to John B. Fish and Mary H. Barrett. His father was an iron founder. The family lived in Lowell, Massachusetts, until the 1850s, when they moved to Manchester, New Hampshire. By the early 1860s, he was also working as an iron founder.
He enlisted in the Union army on August 20, 1861, and he mustered in as a private in the 1st New Hampshire Light Artillery on September 26. According to his service records, he was 5 feet, 8 inches tall, with brown hair and blue eyes. The regiment took part in the Second Battle of Bull Run, the Battle of Antietam, and the Battle of Fredericksburg. Fish was mortally wounded at Fredericksburg on December 13, 1862, and he died the following day.