Over the last decades, Lattice Boltzmann method (LBM) has become a popular method both in academia and industry thanks to its low computational cost for high-fidelity simulations. One of its disadvantages, such as stability issues at high Mach compressible flows, has been gradually overcome, allowing it to capture shocks on fixed geometries such as bumps, NACA airfoils, and M6 wings. However, no LBM method is still able to capture accurately sustained shock on moving geometries such as rotors or turbofans. Recently, a LBM framework was developed to simulate high Mach compressible flows over rotating geometries, but it still showed limited capabilities and to capture shocks over the rotating surfaces. This work investigates the shock wave interaction with rotating geometries using the LBM. The momentum is transported using the hybrid recursive regularized LBM model (HRR), and temperature is solved using the finite-volume method of total energy equation. The rotating overset grids are used to actualize rotating geometries that require interpolation between rotating and fixed grids, as well as fictitious forces within the rotating region. In this work we examine the impact of various numerical methods on capturing shock structures over rotating surfaces. First, we compare the coupling of the total energy equation and the entropy equation with the LBM framework. The total energy equation which has better conservative properties than the entropy equation, is adapted to a rotating non-inertial reference axis. Furthermore, we investigate the effect of higher order MUSCL-Hancock schemes as well as various LBM boundary conditions on rotating surfaces to effectively account for discontinuous shock surfaces.