Thompson was born in Jersey, Licking County, Ohio on March 8, 1848. His parents were Adna Thompson, and Nancy D Thompson. He had a brother named Olvid. In his adolescence he became a skilled carpenter. In 1873 he began operating a grocery store in Elkhart, Indiana. There he began designing a device to manufacture seamless hosiery. He made a fortune in that business, but failing health forced him to quit it.
Thompson is best known for his early work developing roller coasters and for inventing the scenic railway genre of rides. He is known as the "Father of the American Roller Coaster" and is often also called the "Father of the Gravity Ride". Over his lifetime, Thompson accumulated nearly thirty patents related to roller coaster technologies. An example is the patent granted December 22, 1884 for the Gravity Switch-back Railway. Thompson's work built upon an earlier patent for an "Inclined Railway" by John G. Taylor, and upon the general idea of gravity-powered inclined rides dating back to at least the 17th century through the overall history of the roller coaster. Thompson's breakthrough ride was the "Gravity Pleasure Switchback Railway", which opened at Coney Island in 1884. A ride cost 5 cents. In 1887, along with designer James A. Griffiths, he opened the Scenic Railway on the Boardwalk in Atlantic City, N.J. Thompson's scenic railway concept initially was intended to give riders a scenic view of the surrounding landscape; later, Thompson created elaborate painted backgrounds and scenes so that riders would feel like they were touring the Swiss Alps or other foreign landscapes. Thompson was managing director of the L. A. Thompson Scenic Railway Company, 220 West 42nd St., incorporated in 1895. Thompson's scenic railways were immensely popular during the first and second decade of the 1900s, and his company operated six major scenic railways at Coney Island alone during that time. Dozens of scenic railways operated throughout the U.S. and in Europe. Eventually, the scenic railway was eclipsed by faster and more thrilling roller coaster rides made possible by improvements in roller coaster safety technology. Thompson died at his home, Thompson Park, Glen Cove, Long Island, on May 8, 1919 at age 71.