Lindsay was born on November 29, 1900, in Mississippi, where he worked in the cotton fields as a youth. He left Mississippi as a teenager and enrolled in a school in Pittsburgh, Pennsylvania. He then moved to Arizona, where he joined the Army and served in the 10th Cavalry and the 25th Infantry. As part of an Army program, he studied business administration at the University of Arizona. He moved to Los Angeles in 1923 or 1924 and became a City Hall janitor with the Los Angeles Department of Water and Power. He took a civil service exam for a clerkship, and he was given a basement office because, he said, his superiors did not want him to sit with whites. He took classes in governmental administration and political science at the University of Southern California and in business administration at UCLA during the 25 years he worked for the department.