On July 21, 1969, Lillie Belle Allen was a young African American woman from Aiken, South Carolina driving through York, PA to NYC. According to an FBI report (see link below), The car in which Ms. Allen was riding approached a white neighborhood, and their car was attacked by gunfire. In the report, white state troopers were suspected to be in the white mob attacking the car. Ms. Allen died from wounds descibed from a high power rifle.

So, by using "Lilly Belle" in Southern Man it seems reasonable that Neil Young was stating that nothing has changed from the Civil War to present day.