Pre-chamber spark-ignition (PCSI) is a leading advanced ignition concept for internal combustion engines with the potential to enable diesel-like efficiency in medium-duty/heavy-duty (MD/HD) natural gas (NG) engines. By leveraging distributed ignition sources from multiple turbulent jets, the PCSI technology can deliver extremely short combustion duration in ultra-lean mixtures and significantly improve the engine thermal efficiency. However, in the automotive industry there is a lack of adequate science base and predictive simulation tools required for commercial development of PCSI engines. In this study, Reynolds-Average Navier-Stokes simulations are carried out to describe the combustion process in lean-burn NG engines, focusing on the combustion modeling approach. Two combustion models, multi-zone well-stirred reactor (MZ-WSR) and G-equation, are used to simulate the combustion process in an MD NG engine equipped with a fueled-PCSI system for four operating conditions close to the lean operating limit. A skeletal chemical mechanism and a laminar flame speed tabulation are used to compute the combustion accurately. Simulation results are compared with experimental data regarding measured cylinder pressure, heat release rate, and combustion duration. By dividing the PCSI combustion process into four distinct phases, the difference between the two models’ results for each phase is analyzed in detail. The MZ-WSR model overestimates the combustion duration for early flame kernel growth in the pre-chamber due to the lack of a specific formulation to take turbulence-chemistry interaction into account. Despite the prolonged combustion duration and low pressure built-up inside the pre-chamber, the model matches the combustion rate in the main-chamber. In contrast, the G-equation model delivers good agreements for the pre-chamber combustion and turbulent jet-driven combustion processes. However, the model starts to underestimate the combustion rate in the main-chamber, especially under ultra-lean mixture conditions. Finally, improvements are needed for both models to simulate the later combustion stage that occurred in the near-wall regions.