In this work, the friction anisotropy of hexagonal MoS2 (a well-known lamellar compound) was theoretically investigated. A molecular dynamics method was adopted to study the dynamical friction of two-layered MoS2 sheets at atomistic level. Rotational disorder was depicted by rotating one layer and was changed from 0° to 60°, in 5° intervals. The superimposed structures with misfit angle of 0° and 60° are commensurate, and others are incommensurate. Friction dynamics was simulated by applying an external pressure and a sliding speed to the model. During friction simulation, the incommensurate structures showed extremely low friction due to cancellation of the atomic force in the sliding direction, leading to smooth motion. On the other hand, in commensurate situations, all the atoms in the sliding part were overcoming the atoms in counterpart at the same time while the atomic forces were acted in the same direction, leading to 100 times larger friction than incommensurate situation. Thus, lubrication by MoS2 strongly depended on its interlayer contacts in the atomic scale. According to part I of this paper [Onodera, T., et al. J. Phys. Chem. B 2009, 113, 16526 -16536], interlayer sliding was source of friction reduction by MoS2 and was originally derived by its material property (interlayer Coulombic interaction). In addition to this interlayer sliding, the rotational disorder was also important to achieve low friction state.