The present study investigates the applicability of the inlet boundary species Lewis number (combined effect of molecular and flow diffusion) for the nonpremixed moderate and intense low oxygen dilution (MILD) flames. A modified reactive solver named modifiedReactingFoam is developed by including the enthalpy flux in the energy equation and using modified model constants in OpenFOAM. The present solver is tested on the delft-jet-in-hot-coflow burner operating under a moderate and intense low oxygen dilution combustion environment. Along with the flame with Reynolds number 4100, eight other jet-in-hot-coflow flames are simulated to test the capability of the present proposed solver. The main aim of the current work is to investigate the efficacy of the proposed solver in predicting the velocity field, temperatures, and flame lift-off height for the considered flames with a significant reduction in computational time. The predictions with the modified eddy dissipation concept model are improved. However, a significant deviation is still observed in the downstream direction of the burner. The numerical simulations are performed with methane Lewis numbers of 0.9-1.14 by keeping the respective constant Lewis numbers for the inlet boundary species. The modifiedReactingFoam predictions at a methane Lewis number of 1.12 are in very close agreement with the experimental results. The maximum deviation in lift-off heights is within ±3% of the experimental results. The present modified solver outperformed the other combustion models in the literature and reduced the computational time up to 10 times with a combination of DLBFoam compared to the inbuilt solver.