The flow properties of liquid in microchannel have received more attention for their wide applications in different fields. Up to now, little work has focused on the flow behaviors of liquid metals. Recently, liquid lithium (Li) has been considered as one of the candidate plasma-facing materials (PFMs) because of its excellent properties in fusion reactor applications. Considering an accident condition, liquid Li may contact Cu components and erode them, which may cause a serious disaster. The study of the flow properites of liquid Li in Cu microchannel is crucial for the safe application of liquid Li working as a PFM. With the method of non-equilibrium molecular dynamics simulations, in this paper we investigate the flow behavior of liquid Li flowing in Cu microchannels. The density and velocity distributions of Li atoms are obtained. The influence of the dimension of Cu microchannel on the flowing behavior of liquid Li is studied. Comparative analyses are made in three different fluid-solid interfaces, i.e., Li-Cu(100), Li-Cu(110) and Li-Cu(111), respectively. Results show that the density distributions of liquid Li near the interface present an orderly stratified structure. Affected by a larger surface density, a more obviously stratification is found when Li atoms are near the fluid-solid interfaces of Li-Cu(100) and Li-Cu(111) and a wider vacuum gap appears between Li atoms and Cu(111) interface. When Li atoms are near the Li-Cu(110) interface, a lower stratification can be found and an alloy layer appears at Li-Cu(110) interface. Because of its lower surface density, Li atoms spread into the bulk Cu more easily. However, the density distributions have little difference when Li atoms are close to the same fluid-solid interface but with different flow directions. The velocity of Li atoms in microchannel has a parabolic distribution. Because there exists a wider vacuum gap and stratified structure, the Li atoms closed to the Li-Cu (111) interface have the largest velocity. Closed to the Li-Cu (110) interface, Li atoms have the smallest velocity because of the alloy layer and the lower stratified structure. Owing to the diversity of the atomic configurations of Cu (110) face, the liquid Li atoms flow with diverse velocities in different directions on the Li-Cu (110) interface. It is also found that the magnitude of flowing velocity of liquid Li is proportional to the square of microchannel dimension and increases with it. When liquid Li is flowing on the Li-Cu(100) interface, the simulation result reveals that the relationship between microchannel dimension and the largest velocity of Li atoms is in good agreement with Navier-Stokes theory result. It is noteweathy that the present result is smaller than the theoretical result when a negative slip occurs at the Li-Cu(110) interface. In contrast, the result is greater than the theoretical result in the presence of a positive slip at Li-Cu(111) interface.