The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Moller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing "bond"-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids. (c) 2011 American Institute of Physics. [doi:10.1063/1.3595514]