The potential energy curve (PEC) for the first excited state (A2Π) of LiAr is calculated using the multireference configuration interaction method in combination with the basis set, ang-cc-PCVQZ. The Davidson correlation (+Q) and the scalar relativistic effect (+DK) are taken into account in the calculations. And PEC is fitted to analytical Hartree-Fock-dispersion potential function, thereby determining the spectroscopic parameters. These obtained parameters are in excellent agreement with the available experimental and theoretical values. By solving the radial Schrödinger equation of nuclear motion, the vibration levels, rotary inertia and six centrifugal distortion constants (Dv, Hv, Lv, Mv, Nv, Ov) are obtained for the first time. The elastic collisions between the excited-state Li and the ground-state Ar atoms are investigated at low and ultralow temperatures when the two atoms approach to each other along the LiAr (A2Π ) interaction potential. The total and various partial-wave cross sections are calculated at energies from 1.0×10-12 to 1.0×10-3 eV by numerical calculation. The effect of each partial-wave cross section on the total elastic cross section is discussed carefully. The results show that the total elastic cross section is very large and almost constant at ultralow temperatures, and its shape is mainly dominated by the s-partial wave. But with the increase of collision energy, contribution of s-partial wave to the total cross section decreases and the contribution of higher-order partial wave to scattering cross section increases gradually.