The transport and management of oxygen bubbles significantly impact the performance of proton exchange membrane water electrolyzers (PEMWE). The 3D structures of sintered and fibrous PTLs were reconstructed using randomly distributed spherical particles and layer-by-layer generated cylindrical fibers, respectively. The two-phase flow dynamic behavior of oxygen in the PTL and flow channel with lateral velocity were simulated based on the lattice Boltzmann method with a free surface model. At the bottom of the computational domain, spherical bubbles were added at random positions at specified intervals, corresponding to different current densities. The bubble radius can follow the predicted growth law R(t) = β*t^b. The effects of bubble generation timestep interval, contact angle, initial flow velocity, graded porosity and microporous layer structure are investigated. The similarities and differences between spherical and fibrous PTLs are analyzed in detail. The results demonstrate the feasibility and necessity of operating PEMWE at high current densities. Hydrophilic PTLs facilitate the upward movement of oxygen bubbles, with an optimal contact angle range observed. Maximizing the flow channel velocity within laminar conditions promotes the lateral expulsion of bubbles. Compared to spherical PTLs, fibrous PTLs are more suitable for high current density operations. Reducing the porosity or decreasing the fiber diameter near the catalyst layer side can effectively minimize bubble accumulation. Chemical reaction source terms are also implemented into the governing equations on plan, facilitating the potential coupling with electrochemical reactions.