We consider the lattice-gas modeling of simple A + A and A + B electrochemical Langmuir-Hinshelwood surface reactions and compete exact Monte Carlo cyclic voltammograms with those obtained in the mean-field and quasi-chemical or cluster approximations. For AS A reactions, we demonstrate the importance of local correlations between adspecies when a repulsive interaction between neighboring species exists. The mean-field approximation (MFA) cannot account for such local correlations (i.e, ordered adlayers), whereas the quasi-chemical approximation gives results quite close to the Monte Carlo simulations. For the A + B reaction, poor mixing caused by low surface mobility of the adspecies, may result in local correlations (island formation) that cannot be treated satisfactorily by the MFA. A cluster approximation is able to partly bridge the gap between the mean-field and Monte Carlo results.