Abstract: This work conducts a systematic and comprehensive theoretical analysis of numerical instability and numerical accuracy verification for the recently proposed lattice Boltzmann method (LBM) with non-equilibrium linearized collision (NLC-LBM). Through the rigorous Chapman–Enskog kinetic expansion method, the NLC-LBM accurately decomposes the nonlinear terms in the collision operator into equilibrium and non-equilibrium components, and then performs consistent linearization on the non-equilibrium components. This treatment not only completely retains the physical essence of fluid flow and ensures the physical accuracy of the simulation, but also effectively suppresses the divergence of high-wave-number modes in numerical calculations, fundamentally improving the numerical instability of traditional methods. This improvement not only significantly enhances the numerical stability under coarse mesh conditions in classical computing scenarios, solving the bottleneck of easy instability in coarse mesh simulation, but also provides a solid theoretical foundation and adaptation support for the currently rapidly developing quantum-classical hybrid linear computing architecture, laying the foundation for the integrated application of LBM and quantum computing. Based on the Von Neumann linearized instability theory, this paper deeply analyzes the local instability characteristics and hydrodynamic dissipation behavior of the NLC-LBM. Through comparative analysis with the standard LBM, it is clearly demonstrated that the stability of the NLC-LBM under coarse mesh conditions is significantly superior to that of the standard LBM, thereby providing a highly stable and reliable collision model for the efficient and stable simulation of complex flows under coarse mesh conditions. To further verify the physical effectiveness and numerical accuracy of the NLC-LBM, this paper conducts systematic numerical simulation research on three classic benchmark cases, including lid-driven cavity flow, natural convection, and vortex pair merging. The results show that under the same coarse mesh conditions, the standard LBM exhibits obvious non-convergence, characterized by non-physical features such as streamline distortion and velocity profile oscillation; while the NLC-LBM can maintain stable convergence of the flow field and accurately capture the flow characteristics. Under fine mesh conditions, both the computational results and numerical accuracy of the NLC-LBM are basically consistent with those of the standard LBM, fully verifying the physical rationality and numerical reliability of the method.