Recent experiments from the Experimental Advanced Superconducting Tokamak (EAST) show that lower hybrid waves (LHWs) can profoundly change the magnetic topology by inducing helical current filaments flowing along magnetic field lines in the scrape-off layer. Here, it is investigated for the first time how these magnetic perturbations caused by LHWs affect the edge plasma transport utilizing the three-dimensional Monte Carlo code EMC3-EIRENE, both in double-null and single-null configurations. The 3D magnetic topology structure is reflected in the plasma properties, due to much stronger parallel field transport compared with cross field diffusion. Good qualitative agreements between simulation results and experimental data from various edge diagnostics demonstrate that the EMC3-EIRENE code now is capable of taking into account the LHW-induced magnetic perturbation fields with both physical and geometrical effects being considered. Combined with experimental observations, the simulation results strongly support that total current amplitude of LHW-induced filaments increases with an increase in LHW input power. It can further deepen the penetration depth of the additional transport channel by extending the stochastic edge layer, and influence the ratio of heat (or particle) flux between split striated and original strike line on divertor targets. The 3D simulation results also indicate that the additional plasma transport channel induced by LHWs can significantly cause the redistribution of heat load between inner and outer divertor targets, which could not be found by the field line tracing method in previous works.