LAMMPS is a widely used molecular dynamics (MD) software package in materials science, computational chemistry, and biophysics, supporting parallel computing from a single CPU core to large supercomputers. The Kunpeng processor features both high memory bandwidth and core density and is therefore an interesting candidate for accelerating compute-intensive workloads. In this paper, we target the Kunpeng multi-core architecture and focus on optimizing LAMMPS for modern ARM-based platforms by using the Lennard-Jones (L-J) and Tersoff potentials as representative case studies. We investigate both common and specific optimization challenges, and present a comprehensive performance analysis addressing four key aspects: neighbor list algorithm design, force computation optimization, efficient vectorization, and multi-thread parallelization. Experimental results show that the optimized potentials achieve speedups of approximately$2 \times$and$5 \times$, reaching$4.55 \times$and$7.04\times$the performance of the original Intel version for L-J and Tersoff, respectively. Both potentials outperform Intel's acceleration library, with a peak performance up to$2.9\times$-$3.5\times$. In terms of parallel efficiency, we evaluate scalability both within a single CPU (small-scale) and across multiple nodes (large-scale). Strong and weak scaling tests within a single CPU show that when the expansion factor is 32 times, parallel efficiency remains above$90\%$. Large-scale weak scaling across multiple nodes achieves up to$86\%$efficiency when the expansion factor is 32. Using 32 nodes (18,432 processes), our implementation enables billion-atom simulations with L-J and Tersoff potentials. This work achieves breakthrough performance and provides critical support for large-scale molecular dynamics in engineering applications.