The concept of an edge flame structure has been adopted to explain the laminar lifted flames in a nonpremixed jet. Two similarity solutions of velocity and fuel concentration have been used to explain flame stability. Recently, it was shown that the experimental results from studies of jet velocities and lift-off heights could be converted to a relationship between the edge flame speed and the fuel concentration gradient. However, this was not sufficient to explain actual structures and behaviors of lifted flames. In this study, related theories and their similarity solutions were improved to get more realistic results through an efficient process. Experiments were conducted with various parameters such as jet velocity, fuel type, tube diameter, air-premixing ratio, and fuel dilution. Effective mass diffusivities and effective Schmidt numbers were estimated based on the experimental results. Using these values, the theoretical basis for a new relationship between the edge flame speed and the fuel concentration gradient was obtained. It was conclusively found that non-monotonic variation in the edge flame speed occurs. From this, flame structures were classified into three regimes based on flame structures and heights: ordinary edge flame in a lower-regime, merged edge flame in a middle-regime, and premixed flame in a higher-regime. Flame speeds of the ordinary edge flames in the lower-regime were selected for comparison with the results of previous studies. From this work, the relationship between the similarity solutions and the experimental results can now be understood in greater detail, and the deviations due to the flame structure can be distinguished.