Simulations of lithium (Li) impurity transport behaviour with a liquid lithium divertor on the EAST tokamak have been performed using the fluid code EMC3-EIRENE and the Monte Carlo code ITCD. The interactions between particles and the wall surface, like the gyration-induced scrape-off effect, sheath acceleration, kinetic self-sputtering and reflection, are typically ignored or simplified in fluid models. In order to uncover the impacts of the scrape-off effect, sheath acceleration, kinetic self-sputtering and reflection on Li distribution, detailed analysis of the density distributions of Li1+ and Li2+ ions at the divertor region have been carried out by ITCD modelling. The newly-upgraded ITCD code can principally reproduce the distribution patterns of Li ions as well as EMC3-EIRENE under identical plasma conditions on EAST. However, due to the scrape-off effect and sheath acceleration, the densities of Li1+ and Li2+ ions simulated by ITCD are evidently reduced compared to the EMC3-EIRENE simulations. The kinetic self-sputtering by redeposited Li particles in ITCD can increase the densities of the Li ions. Moreover, the kinetic reflection database calculated by SRIM code has been employed by ITCD, which leads to an increase in the Li densities compared to the reflection approach used in EMC3-EIRENE. Overall, by adding the aforesaid physical effects in ITCD, the total number of Li ions shows an obvious reduction compared to the EMC3-EIRENE modelling.