We explore simple lattice-gas reaction models for CO-oxidation on 1D and 2D periodic arrays of surface adsorption sites with CO adsorption and desorption, dissociative O2 adsorption and recombinative desorption (at low rate), and CO + O reaction to form CO2. Adspecies interactions are neglected, and adspecies diffusion is effectively absent. The models are motivated by studies of CO-oxidation on RuO2(110) at high-pressures. Despite the lack of adspecies interactions, negligible adspecies diffusion results in kinetically induced spatial correlations. A transition occurs from a random primarily CO-populated steady-state at high CO-partial pressure, pCO, to a strongly correlated near-O-covered steady-state for low pCO as noted by Matera et al. [J. Chem. Phys. 134, 064713 (2011)]. In addition, we identify a second transition to a random near-O-covered steady-state at very low pCO. Furthermore, we identify and analyze the slow "diffusive dynamics" for very low pCO and provide a detailed characterization of the crossover to the strongly correlated O-covered steady-state as well as of the spatial correlations in that state.