Branched flow refers to the bifurcation of waves as they propagate through customized disordered media, leading to the creation of multiple channels or branches. This dynamic wave phenomenon has been observed in various disordered systems under specific conditions. In our study, we demonstrate the branched flow of light within a disordered photonic lattice and establish that the intensity distribution of these branches follows Lévy statistics. This behavior is more pronounced when the wavefront of the input light beam is adjusted, resulting in the propagation of more stable branches through the structure. We also investigated the formation of light branches with varying input beam widths and the impact of two simultaneous input beams on the disordered photonic lattice. Our findings indicate that the distribution of branches in the disordered system can be controlled by shaping the wavefront of the input beam, which has potential applications in imaging, nano-lasing, and integrated photonic components. This research opens new avenues for fundamental studies on the manipulation of light through complex photonic systems.