In the present study, a novel Lieb lattice with five points (hereinafter referred to as the Lieb-5 lattice) in the minimum periodic unit is used as a platform. The sites of Lieb-5 lattices are classified into two categories according to their spatial positions, namely, the center and edge lattices. Using the beam-propagation method, we investigate the effects of different intensities of two sets of lattices on out-of-phase octupole-beam propagation. The ratio of the intensities of the two lattice categories is 2∶3; further, according to simulation results for either an on-site or off-site incident, when the intensity of the center lattice is less than that of the edge lattice, as in this case, an eight-peak shape with strong localization is maintained during beam propagation. Otherwise, the beam barely maintains the shape of the eight peaks in the propagation process. The energy between the incident lattices is periodically coupled with the increase of propagation distance, presenting weak localization, because the geometric frustration of the Lieb-5 lattice caused by its unique topological structure inhibits the discrete diffraction of light beams. If the binding property of the lattices, diffraction of the beam, and interaction of the out-of-phase beam stay in balance, the eight-peak structure can be maintained; otherwise, the beam cannot always maintain the eight-peak structure.