For whateer reason, the word "lineback" has been attached to dun. Dun is a gene that dilutes the color of a horse and causes "primitive markings" including leg barring, shoulder barring, and a dorsal stripe. In order for a horse to be a dun it MUST have a dorsal stripe, meaning EVERY dun could be called a "lineback dun."
The name doesn't mean anything. Duns always have a dorsal stripe.