Turbomachinery simulations with rotating components require accurate computational fluid dynamics methods. Lattice Boltzmann methods are attractive for such applications as they have low numerical dissipation, low dispersion, and mesh complex geometries easily using Cartesian grids. The Local Reference Frame (LRF) approach handles rotation by maintaining separate reference frames for static and rotating domains. However, current LRF implementations require uniform grid resolution across the overlap region where the two grids communicate. This prevents local refinement near walls or in wakes, which is problematic for industrial cases. We present a non-uniform LRF method that progressively removes this constraint, allowing mesh refinements of ratio 1:2 to cross the overlap region. The key contribution is the proper rescaling of the non-equilibrium stress tensor when interpolating between different grid levels. This rescaling accounts for both molecular viscosity and subgrid-scale (SGS) contributions in Large Eddy Simulations. We derive the rescaling from acoustic scaling principles and Kolmogorov turbulence theory and use temporal interpolation to synchronize fine and coarse grids. The proposed method is validated on three test cases: Taylor–Couette flow, two-dimensional rotating cylinders (Re=200,0.5≤α≤3.0), and three-dimensional turbulent flow past a rotating cylinder (Re=5000,α=1.0). Aerodynamic coefficients agree with uniform LRF within 4%. It is shown that proper SGS rescaling reduces spurious noise significantly. The method aims to enable the simulation of configurations that were previously problematic: installed propellers, shrouded turbines, or any case where rotating geometries operate near static surfaces and require local grid refinement.