For the first time, to our knowledge, we report ray-tracing simulations of an advanced liquid-crystal gradientindex lens structure for application in switchable two-dimensional/three-dimensional (3D) autostereoscopic displays. We present ray-tracing simulations of the angular-dependent lens action. From the results we conclude that the lens action of the advanced optical design corresponds to the desired performance for small viewing angles. For oblique viewing angles of approximately 30°and higher, the lens action becomes significantly weaker compromising the 3D performance of an autostereoscopic display. The general approach and the advanced ray-optics analysis procedures presented form a useful tool in the search for improvements for high viewing angles and enable a better understanding of the liquid-crystal technology discussed.