We performed simulations on in-plane current driven Josephson vortex systems in high- T c cuprates at weak parallel magnetic fields and /or low anisotropies. It is found that the in-plane resistivity is Lorentz-force dependent at small current regime below the melting transition. As the current increases, the Josephson vortex lattice melts dynamically, the Lorentz-force independence of resistivity reappears. These results are possibly related to the experiments on YBCO.