The present study is devoted to the computational modeling of non-premixed flames stabilization in high-velocity reactive flows where compressibility effects, turbulent mixing, and chemical kinetics processes are competing. The characterization of the unsteady features of such turbulent reactive flows is still a difficult task, from both experimental and numerical points of view, so that the evaluation of numerical models capabilities remains essentially performed through the comparisons of steady-state solutions with the corresponding experimental data. The Reynolds averaged Navier-Stokes (RANS) strategy still provides the most suitable framework to obtain such steady-state solutions for flows at a high Reynolds number, especially for design and optimization purposes. In turbulent non-premixed flames, the competition between molecular diffusion effects-namely, micromixing or scalar dissipation-and chemical kinetics must be taken into account. In the present work, a Lagrangian framework, able to represent non-premixed combustion in supersonic turbulent reactive flows, is set forth. The main objective of the study is to assess the relevance of the corresponding model to predict turbulent combustion in high-speed flows. The conclusions are drawn from comparisons with results from a well-documented experimental configuration that consists of a supersonic lifted co-flowing hydrogen-air non-premixed jet flame retained to evaluate the ability of the modeling proposal to describe the conversion of kinetic energy into sensible enthalpy. The comparisons between computational results and experimental data are satisfactory and suggest that, despite their complexity, the main physical processes are well described with the proposed approach.