As an important intermediate step in a long-term project to fully understand the spectroscopy of the three lowest singlet states of LiH, (X 1Σ+, A 1Σ+, and B 1Π), we have constructed accurate hybrid potential energy curves for the X1Σ+ and A1Σ+ states to complement earlier work on the B1Π state. In each case the known Rydberg–Klein–Rees (RKR) for low vibrational levels was joined to the long-range region of the potential (represented by new C6, C8, and C10 coefficients reported herein) fixed by the accurately known dissociation limits. The joining was obtained by scaling slightly the ab initio results of Docken and Hinze in the region of interpolation. Extrapolation to smaller distance was also done using ab initio results.