The coupling of numerical methods in different scales is of great significance in the investigation of intricate multiscale phenomena. This work develops a dynamic coupling approach based on domain decomposition by combining the mesoscale lattice Boltzmann method (LBM) and microscale molecular dynamics (MD) simulations. In the proposed scheme, a two-way concurrent exchange of information between different scales has been achieved. At the atomistic scale, the fluid dynamics are modeled through the particle-based MD method on the framework of the open large-scale atomic/molecular massively parallel simulator (LAMMPS). While at the coarse scale, the fluid system is simulated utilizing the LBM approach, which relies on the collision and streaming of the particles constrained in discretized lattices, adhering to the conservation laws of mass and momentum. The exchange of velocity distributions between the two scales was handled. The accuracy and efficiency of the proposed coupling scheme were validated through simulations of the classic Poiseuille and Couette flows. The obtained results show that satisfactory agreement against pure MD results has been achieved. Moreover, a notable improved efficiency as high as 92.8% has been observed for the coupling scheme in comparison to MD simulations. Due to the inherent parallelism of LBM and MD, the proposed coupling scheme exhibits great potential for extended application in studying complex multiscale phenomena with dynamic coupling between different scales.