Oxidative coupling of methane (OCM) is a promising process for converting natural gas into high-value chemicals such as ethane and ethylene. The process, however, requires important improvements for commercialization. The foremost is increasing the process selectivity to C2 (C2H4 + C2H6) at moderate to high levels of methane conversion. These developments are often addressed at the catalyst level. However, optimization of process conditions can lead to very important improvements. In this study, a high-throughput screening (HTS) instrument was utilized for La2O3/CeO2 (3.3 mol % Ce) to generate a parametric data set within the temperature range of 600–800 °C, CH4/O2 ratio between 3 and 13, pressure between 1 and 10 bar, and catalyst loading between 5 and 20 mg leading to space-time between 40 and 172 s. Statistical design of experiments (DoE) was applied to gain insights into the effect of operating parameters and to determine the optimal operating conditions for maximum production of ethane and ethylene. Rate-of-production analysis was used to shed light on the elementary reactions involved in different operating conditions. The data obtained from HTS experiments established quadratic equations relating the studied process variables and output responses. The quadratic equations can be used to predict and optimize the OCM process. The results demonstrated that the CH4/O2 ratio and operating temperatures are key for controlling the process performance. Operating at higher temperatures with high CH4/O2 ratios increased the selectivity to C2 and minimized COx (CO + CO2) at moderate conversion levels. In addition to process optimization, DoE results also allowed the flexibility of manipulating the performance of OCM reaction products. A C2 selectivity of 61% and a methane conversion of 18% were found to be optimum at 800 °C, a CH4/O2 ratio of 7, and a pressure of 1 bar.