The ab initio quadratic CI calculation method and the effective-core-potential basis set have been used to calculate the equilibrium geometries, potential energy curves, dissociation energies of the ground state, and low-lying electronic states of Lu-2 for the first time. The symmetries of these states are determined by analyzing the potential energy curves and optimization calculations at the same time. The analytical potential energy functions of these states have been fitted with the Murrell-Sorbie potential energy function from the calculated values with the ab initio method. The spectroscopic parameters of each state are calculated through the relationship equations between analytical potential energy function and spectroscopic parameters, and are compared with some other theoretical and experimental data available from the experiment at present. For the ground state, we obtain the symmetry is X (3)Sigma(g), omega(e)=113.3 cm(-1) with omega(e)chi(e)=0.16 cm(-1), leading to a spectroscopic dissociation energy of 1.79 eV. They are in agreement with the recent experiments.