A new methodology for modeling and simulation of reactive flows is reported in which a 3D formulation of the Linear Eddy Model (LEM3D) is used as a post-processing tool for an initial RANS simulation. In this hybrid approach, LEM3D complements RANS with unsteadiness and small-scale resolution in a computationally efficient manner. To demonstrate the RANS-LEM3D model, the hybrid model is applied to a lifted turbulent N2-diluted hydrogen jet flame in a vitiated co-flow of hot products from lean H2/air combustion. In the present modeling approach, mean-flow information from RANS provides model input to LEM3D, which returns the scalar statistics needed for more accurate mixing and reaction calculations. Flame lift-off heights and flame structure are investigated in detail, along with other characteristics not available from RANS alone, such as the instantaneous and detailed species profiles and small-scale mixing.