Dillon was born in Northampton, Montgomery County, New York. He studied medicine at the University of Iowa at the age of 19. Shortly after beginning to work as a doctor, he switched to studying law, and was admitted to the Iowa bar in 1852. He was elected as the Scott County prosecutor after a brief private practice in 1853, and was then elected to a judgeship in Iowa's 7th Judicial Circuit in 1858. He joined to the Iowa Supreme Court in 1862 and served until 1869, when he was appointed by President Grant to the United States Circuit Court.