The X (2)Sigma (+), A (2)Pi, and B (2)Sigma (+) states of the LiNe molecule have been investigated by the coupled cluster approach, in conjunction with a series of increasing size augmented correlation-consistent basis sets of double through sextuple zeta quality. For the A (2)Pi bound state the convergence properties of the binding energy and spectroscopic constants were examined as a function of the basis set size. It was found that at the extrapolated complete basis set limit all our findings are in excellent agreement with experiment, under the proviso, however, that basis set superposition effects have been carefully considered.