Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb+ and Li+ cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R-e, D-e, T-e, omega(e), omega(e)x(e), and B-e) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)E(+), 8-10(3)Sigma(+), 6(1,3)Pi, and 3(1,3)Delta excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li-Rb+ and Li+Rb- arrangements. The diabatic potential energy for the (1,3)Sigma(+), (1,3)Pi, and (1,3)Delta symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.