Lindsay Young was born to Robert Smead and Lillie Young on January 13, 1913. He entered the University of Tennessee in 1930 and graduated with his Bachelor of Laws on June 3, 1935. After graduation, Young joined the law firm of Baker, Young, Young, and Baker (headed by Tennessee Representative Howard H. Baker Sr.) and specialized in corporate law. He later became a partner in McCampbell and Young, where he practiced law with his twin brother, Robert Smead Young, Jr. Lindsay Young also served on the boards of several local organizations, including the East Tennessee Foundation, the Knoxville Museum of Art, the Knoxville Opera Company, the Knoxville Symphony Society, and Knoxville College.

As a result of his investments, Lindsay Young was also one of the wealthiest men in Knoxville. He donated this wealth freely to numerous local organizations, including the Knoxville-Knox County Animal Center (now called the Young-Williams Animal Center in honor of its two most generous donors), the Knoxville YMCA, and the University of Tennessee. One of Young's donations to the University established the Lindsay Young Endowment, which provides the University Libraries with funds to purchase research materials in the humanities. Young died on February 9, 2006 in Knoxville, Tennessee.