Partial quenching structure of diffusion flames in a turbulent mixing layer has been investigated by the method of flame hole dynamics in oder to develope a prediction model for the phenomenon of turbulent flame lift off. The present study is specifically aimed to remedy the shortcoming of the stiff transition of the conditioned partial burning probability across the crossover condition by employing the level-set method which enables us to include the effect of finite flame edge propagation speed. In light of the level-set simulation results with two models for the edge propagation speed, the stabilizing conditions for turbulent lifted flame are suggested. The flame hole dynamics combined with the level-set method yields a temporally evolving turbulent extinction process and its partial quenching characteristics is compared with the results of the previous model employing the flame-hole random walk mapping based on three critical scalar dissipation rates. The probability to encounter reacting state, conditioned with scalar dissipation rate, demonstrated that the conditional probability has a rather gradual transition across the crossover scalar dissipation rate. Such a smooth transition is attributed to the finite response of the flame edge propagation.