Flame stabilization is the key to extending scramjets to hypersonic speeds; accordingly, this topic has attracted much attention in theoretical research and engineering design. This study performed large eddy simulations (LESs) of lifted hydrogen jet combustion in a stepped-wall combustor, focusing on the flame stabilization mechanisms, especially for the autoignition effect. An assumed probability density function (PDF) approach was used to close the subgrid chemical reaction source. The reliability of the solver was confirmed by comparing the LES results with experimental data and published simulated results. The hydrogen jet and the incoming stream were first mixed by entraining large-scale vortices in the shear layer, and stable combustion in the near-wall region was achieved downstream of the flame induction region. The autoignition cascade is a transition of fuel-rich flame to stoichiometric ratio flame that plays a role in forming the flame base, which subsequently causes downstream flame stabilization. Three cases with different jet total temperatures are compared, and the results show that the increase in the total temperature reduces the lift-off distance of the flame. In the highest total temperature case, an excessively large scalar dissipation rate inhibits the autoignition cascade, resulting in a fuel-rich low-temperature flame.