The effects of adding hydrogen to methane were investigated through the transition between laminar and turbulent regimes based on the characteristics of non-premixed lifted flames. Lift-off heights can show complex trends depending on the fuel tube diameter, jet velocity, and hydrogen ratio. In the laminar regime, the lift-off heights were smaller than the laminar mixing core and decreased with hydrogen addition. In the turbulent regime, the lift-off heights could be much smaller or larger than the turbulent core when the jet velocities were smaller or larger than specific criteria, respectively. Such transitional phenomena were discussed based on the theories related to flow development, premixed flame, and edge flame structures. These included the mixing layer, quenching distance, flow re-direction, Damköhler number, turbulent flame speed, etc. Meanwhile, existing relationships between the lift-off heights and the flow velocities showed significant deviations when the hydrogen ratio was large. An improved relationship between the lift-off heights and the fuel jet velocities was proposed, considering the influence of the virtual origin and the flammable mixing layer. This relationship will apply to various fuel compositions such as propane, methane, hydrogen, and their mixtures. In addition, the blow-off mechanism was explained based on the turbulent burning velocity. Finally, the overall stabilization modes and mechanisms of the lifted flames were explained.