In the realm of geometric algebra and robotics, understanding the mathematical structures that describe motion is paramount. In Euclidean space, dual quaternions have emerged as a powerful tool for representing rigid body motions, encapsulating both rotation and translation in a compact, efficient manner. This elegance extends into the Lorentzian space, where dual split quaternions serve a similar role, adapting to the unique geometric properties of spacetime. This paper delves into the theory and application of dual split quaternions in representing line symmetric motions within Lorentz space, illustrating their utility and elegance in handling complex motion representations.