Wearable robotic systems are being developed to prevent injury to the low back. Designing a wearable robotic system is challenging because it is difficult to predict how the exoskeleton will affect the movement of the wearer. To aid the design of exoskeletons, we formulate and numerically solve an optimal control problem (OCP) to predict the movements and forces of a person as they lift a 15 kg box from the ground both without (human-only OCP) and with (with-exo OCP) the aid of an exoskeleton. We model the human body as a sagittal-plane multibody system that is actuated by agonist and antagonist pairs of muscle torque generators (MTGs) at each joint. Using the literature as a guide, we have derived a set of MTGs that capture the active torque-angle, passive torque-angle, and torque-velocity characteristics of the flexor and extensor groups surrounding the hip, knee, ankle, lumbar spine, shoulder, elbow, and wrist. Uniquely, these MTGs are continuous to the second derivative and so are compatible with gradient-based optimization. The exoskeleton is modeled as a rigid-body mechanism that is actuated by a motor at the hip and the lumbar spine and is coupled to the wearer through kinematic constraints. We evaluate our results by comparing our predictions with experimental recordings of a human subject. Our results indicate that the predicted peak lumbar-flexion angles and extension torques of the human-only OCP are within the range reported in the literature. The results of the with-exo OCP indicate that the exoskeleton motors should provide relatively little support during the descent to the box but apply a substantial amount of support during the ascent phase. The support provided by the lumbar motor is similar in shape to the net moment generated at the L5/S1 joint by the body; however, the support of the hip motor is more complex because it is coupled to the passive forces that are being generated by the hip extensors of the human subject. The simulations developed in this study are specific to lifting motion and a lower back exoskeleton. However, the framework is applicable for simulating a large range of robotic-assisted human motions.