Abstract In light of the global commitment to decarbonize industrial processes, carbon capture and storage (CCS) plays a pivotal role in mitigating greenhouse gas emissions from gas turbine (GT) power generation processes. Achieving an efficient GT–CCS coupling requires the employment of high percentages of exhaust gas recirculation (EGR) to maximize the CO2 content at the CCS inlet. Nevertheless, such operating conditions pose critical challenges for conventional combustion systems due to reduced oxygen levels associated with higher EGR, limiting engine operability. To address this challenge, the development of innovative technical solutions is essential to extend the combustor operational capabilities at high EGR rates. For this goal, a significant number of computational fluid dynamics (CFD) simulations are required to identify the flame stability limits across various EGR levels and burner designs. It is imperative, in this context, to minimize computational costs while maintaining high accuracy. In this work, a comprehensive comparative study of an extended version of the flamelet generated manifolds (FGM) and the artificially thickened flame (ATF) model is performed through a large eddy simulation (LES)-based CFD analysis. The investigation is performed within the context of an industrial lean-premixed burner manufactured by Baker Hughes, operating with natural gas and CO2-diluted air at atmospheric pressure. While the extended-FGM has been previously presented by the authors in a study on the same test rig under standard air conditions, the current work aims to extend its application to critical oxygen-depleted conditions, where near-blowout phenomena such as flame liftoff and length elongation may become significantly pronounced. Numerical validation is carried out through a direct comparison of the computed averaged heat release, representing the flame topology, with detailed OH* chemiluminescence images from a test campaign conducted by the technology for high temperature (THT) Lab of the University of Florence. The experimental data will serve as the primary benchmark for assessing the models’ effectiveness in capturing the main dynamics of such critical operating conditions. Furthermore, potential disparities in both thermal and flow fields at the burner exit region between the two models will be discussed.