The kinetics of the CH4/O2 reaction, occurring on post-combustion catalysts to treat the exhaust gases of natural gas-powered engines, has been investigated in lean conditions on model Pd catalysts supported on K-doped LaMnO3. Experimental and predicted reaction rates have been compared according to a single site on Pd active sites and dual site reaction mechanism on active sites located at the Pd-perovskite interface. Comparisons with a benchmark Pd/LaMnO3 emphasized significant changes induced by thermal aging at 750 °C in wet atmosphere (10 vol% H2O in 5 vol% O2). Indeed, the contribution of the single site mechanism grows on aged Pd/LaMnO3 emphasizing a deterioration of the Pd-LaMnO3 interface. The opposite trend is observed on Pd/La1−xKxMnO3 with kinetics obeying to a single site mechanism on pre-reduced catalyst and then shifting to a quasi-exclusive dual site mechanism after aging. Such kinetic features have been discussed with respect to bulk and surface physicochemical characterization pointing out the key role of potassium in the stability of the Pd-support interface.