The effects of oscillations in gas composition, known as lean/rich dithering, on the performance of a commercial Pd-based three-way catalyst (TWC) for stoichiometric natural gas (NG) engines were evaluated using synthetic exhaust flow reactor experiments. Under simulated NG exhaust conditions, NO conversion was intimately correlated to CH4 conversion at slightly fuel-rich operating conditions. CH4 conversion significantly varied with lambda (or O-2 concentration) and depended on the direction of the lambda change. The dynamic CH4 conversion is likely related to the change of catalyst oxidation state and structures of Pd active sites. The CH4-NO cross-over point was found at a rich-biased lambda rather than stoichiometry. Compared to static operation, catalyst performance was much higher under a realistic dithering condition. The impacts of dithering parameters including amplitude and frequency on CH4 and NO conversions were explored. O-2 dosage is proposed as an effective descriptor of the TWC dithering performance. In the O-2-dosage space, the performance of distinct dithering parameters collapse, helping to elucidate the fundamental influence of dithering parameters on TWC performance. With the help of O-2 dosage, an optimal operating window leading to high CH4 and NO conversions was identified. A higher dithering amplitude is required to keep the catalyst in a reduced state for higher CH4 and NO conversions, while an appropriate O-2 dosage that does not exceed the breakthrough OSC is necessary to avoid excess O-2 that results in NO slip. The dithering amplitude and O-2-dosage-metric maps provide a new method for studying dynamic TWC performance and identifying optimum operation strategies.