The X (2)Sigma(+), A (2)Pi, and B (2)Sigma(+) states of the LiAr and LiKr molecules have been examined theoretically employing the coupled cluster method combined with augmented correlation consistent basis sets of double through sextuple zeta quality. After constructing basis set superposition error-free potential energy curves for the above states, dissociation energies (D-e), bond distances (r(e)), and common spectroscopic parameters are extracted through the numerical solution of the one-dimensional rovibrational Schrodinger equation. For the "bound" A (2)Pi states of LiAr and LiKr, the D-e values can be considered in harmony with experimental values: D-e=890.4 (957+/-30) and 1220.0 (1200) cm(-1) (experimental values in parentheses), respectively. Corresponding bond lengths, r(e)=2.545 (2.50+/-0.08) and 2.673 (3.27) Angstrom indicate that the experimental bond distance of the LiKr A (2)Pi state is rather too large.