Lester Paige Breckenridge was born May 17, 1858 in Meriden, Connecticut to Moses P. and Lucretia (Wetherell) Breckenridge. He graduated from Yale's Sheffield Scientific School in 1881. He married May Brown on December 19, 1883 in Memphis, Tennessee. The couple had three children: Blanche F. (born 10-14-1884), Gladys S. (born 5-19-1888), May Harding (born 6-5-1890). Breckenridge was an instructor in the mechanical engineering department at Lehigh University in Bethlehem, Pennsylvania from 1882-1884 and from 1886-1891. He was appointed at Michigan Agricultural College on August 24, 1891 as a professor of mechanical engineering and Director of the Shops. While at MAC, he worked on the college's exhibit at the 1893 World Fair in Chicago. In 1893 he left MAC for a position at the University of Illinois' Champaign-Urbana Campus as head of the department of mechanical engineering, where he was instrumental in creating an engineering experiment station in 1903. He served as the first director of the station from 1905-1909. He accepted a position at Yale in 1909 as professor of mechanical engineering, where he remained until his retirement in 1923 as professor of mechanical engineering emeritus. He became the first honorary member of Tau Beta Pi on November 5, 1892 on MAC's campus and later became the president of the organization's executive council. Breckenridge was also a member of the American Society of Mechanical Engineers, the Western Society of Engineers, the Society for Promotion of Engineering Education, the St. Louis Railway Club and the Western Railway Club.

He died August 22, 1940 in Charlotte, Vermont and is buried in Westfield, Massachusetts.