The autonomous control of landing procedures can provide the efficiency and precision that are vital for the successful, safe completion of space operations missions. Controlling a lander with this precision is challenging because the propellants, which will be expended during the operations, represent a significant fraction of the lander's mass. The mass variation of each tank profoundly influences the inertia and mass characteristics as thrust is generated and complicates the precise control of the lander state. This factor is a crucial consideration in our research and methodology. The dynamics model for our lander was developed where the mass, inertia, and center of mass (COM) vary with time. A feed-forward neural network (NN) is incorporated into the dynamics to capture the time-varying inertia tensor and COM. Moreover, the propellant takes time to travel through the feed lines from the storage tanks to the engine; also, the solenoid valves require time to open and close. Therefore, there are time delays between the actuator and the engine response. To take into account these sources of variations, a combined time delay is also included in the control loop to evaluate the effect of delays by fluid and mechanisms on the performance of the controller. The time delay is estimated numerically by a Computational Fluid Dynamics (CFD) model. As part of the lander's control mechanism, a thrust vector control (TVC) with two rotational gimbals and a reaction control system (RCS) are incorporated into the dynamics. Simple proportional, integral, and derivative (PID) controllers are designed to control the thrust, the gimbal angles of the TVC, and the torque required by the RCS to manipulate the lander's rotation and altitude. A complex mission with several numerical examples is presented to verify the hover and rotational motion control.