Lizards run quickly and stably in a bipedal gait, with their bodies exhibiting a lateral S-shaped undulation. We investigate the relationship between a lizard's bipedal running and its body movement with the help of a dynamic simulation. In this study, a dynamic theoretical model of lizard is assumed as a three-link consisting of an anterior and posterior bodies, and a tail, with morphometrics based on Callisaurus draconoides. When a lizard runs straight in a stable bipedal gait, its pelvic rotation is periodically synchronized with its gait. This study shows that the S-shaped body undulation with the yaw motion is generated by minimizing the square of joint torque. Furthermore, we performed the biomechanical simulation to figure out the relationship between the lizard's lateral body undulation and the bipedal running locomotion. In the biomechanical simulation, all joint torques significantly vary by the waist and tail' motions at the same locomotion. Besides, when the waist and tail joint angles increase, the stride length and duration of the model also increase, and the stride frequency decreases at the same running speed. It means that the lizard's undulatory body movements increase its stride and help it run faster. In this study, we found the benefits of the lizard's undulatory body movement and figured out the relationship between the body movement and the locomotion by analyzing the dynamics. In the future works, we will analyze body movements under different environments with various simulators.