The correlation energy in LiH and LiH+ molecules is studied as a function of bond distance, from the united atom limit to the complete bond dissociation, using customized basis sets and Full Configuration Interaction. The analysis reveals an unusual complexity of the correlation energy dependence on the bond distance. The obtained accurate correlation energy profiles are used to study the performance of the established correlation models. The density functional models are found to be reasonably accurate in the description of LiH molecule, and are deficient in LiH+.