Stabilization mechanisms of lifted laminar propane flames are investigated in an axisymmetric jet flow configuration. Detailed mixing and flow fields upstream of the flame lift-off heights measured by Chung and coworkers [28-30] are calculated on a nonreacting flow basis. The local stoichiometric axial velocity, U-st, and scalar dissipation rate, chi(st), are obtained at points that are upstream of the stabilization locations by a redirection region length. Variation is investigated with jet exit velocity, nozzle diameter, coflow air velocity as well as partial jet premixing with air. It is found that U-st decreases consistently with increasing chi(st) when the centerline mixture fraction is higher than that of the rich flammability limit. Beyond this threshold, a rich-joined flame is formed at downstream locations with U-st independent of the local scalar dissipation rate. Instead, U-st decreases with increasing zeta(st), the stoichiometric mixture fraction of the jet flow. For lifted flames stabilized close to the burner exit with an edge-flame appearance, the maximum attainable mixture fraction gradient approaches that calculated for extinction of stretched diffusion flames in the counterflow geometry. The flame propagation velocity remains positive. The trend of decreasing U-st with increasing chi(st) is also found for numerical simulations with a unity Lewis number [18] and for experimental data of lifted methane flames [19]. These results corroborate the triple flame stabilization concept. An empirical formula for the triple flame propagation velocity is proposed with a nonlinear dependency on local scalar dissipation rate. In addition, different flame stabilization mechanisms previously proposed for lifted turbulent diffusion flames are reconciled for lifted laminar flames, depending on the local flow/mixing conditions. Appropriate flame stability and blow-out criteria are derived and these predict the flame lift-off height and blow-out velocity accurately. Implications for flame stabilization in turbulent jet flows with such triple flame structures are also discussed.