The laminar flamelet approach is frequently applied to model turbulent non-premixed flames based on the assumption of adiabatic combustion. This generally results in the significant overprediction of temperatures for flames where thermal radiation is important. In the present study, an adiabatic, mixedness-reactedness flamelet combustion model has been extended to incorporate the effect of radiation heat transfer using the concept of enthalpy, defect. This requires the generation of flamelet data sets using a detailed chemical kinetic mechanism and introduction of enthalpy defect as an additional flamelet parameter. The methodology developed has been applied to simulate lifted, free, turbulent non-premixed natural gas flames for which measurements are reported in the literature. A non-adiabatic flamelet data library for methane-air flames has been generated with the GRI reaction mechanism using the modified CHEMKIN code for the modeling of turbulent radiating flames. The turbulent flame computational results, with and without radiation heat transfer, are compared with experimental data for mean gas temperatures, species concentrations and flame lift-off heights for a number of laboratory- and large-scale lifted turbulent jet flames. Predictions obtained using the non-adiabatic flamelet model are found to be in good agreement with temperature measurements, whereas the original adiabatic model significantly overestimates temperatures in the downstream regions of flames where significant heat loss occurs. Species concentration and lift-off height results show small differences between predictions with and without radiation losses in regions close to the base of the flame, although both methodologies provide satisfactory agreement with the available data.