The structures of LiH, LiO and LiOH have been optimized based on the density functional (B3LYP/sdd) method with relativistic effective core potential. The Murrell-Sorbie analytic potential energy functions for LiH and LiO, and the many-body expansion analytic potential energy function for LiOH are derived by using the many-body expansion theory and normal equation fitting methods. The dissociation energies for LiH, LiO and LiOH are calculated from the analytic potential energy functions. Then, the atomic and molecular reaction dynamic processes for the collision of O+LiH(ν=0,j=0) system are investigated with the present potential energy functions by Monte-Carlo quasi-classical trajectory approach. The results show that O+LiH(ν=0,j=0) has no energy threshold, and the dominated product is LiO.