With the forecast of rise in the energy usage, it is imminent that the concentration of toxic emissions such as carbon monoxide (CO) and oxides of nitrogen (NOx) in the ecosystem will increase. One of several industrial techniques to mitigate the emission levels is lean premixed combustion. However, this combustion mode often leads to the problem of Lean Blowout (LBO), which is not well understood. The present study attempts to devise an effective and computation-friendly industrial tool to predict the behavior of lean flames near extinction in a combustion chamber and estimate the lean blowout limits under high temperature and high pressure conditions. Utilizing a tabulated chemistry approach in combination with Reynolds Averaged Numerical Simulation (RANS) turbulence model, extensive validation is performed comparing plain and reacting flow simulation results with the experimental data of laboratory-scale burner at Paul Scherrer Institute (PSI). A modified Flamelet Generated Manifold (FGM) combustion model in conjunction with Reynolds Stress Model (RSM) turbulence model was found to give an accurate prediction of the flow and temperature field inside the combustor. Using this model, the study explores the impact of operational parameters, such as pressure, preheat temperature, turbulence intensity at the inlet and inlet bulk velocity on flame position, temperature, emissions and blowout limits for lean premixed methane-air flames. The combustion model was further applied to the extinguishing flames to study the flame stability limit, which is a very important criterion for an efficient combustor design. The results show that the modified FGM model can reproduce the flame stability curve within 20% of the experimental limit.