Surface-lattice resonances generated by using noble-metallic nanoparticle arrays can effectively suppress radiation loss, thereby improving the resonance quality factor and increasing localized field intensity. Surface-lattice resonances have been widely used for designing high-performance micro-nano photonic devices. Realizing the simultaneous excitation of orthogonal and parallel surface-lattice resonances is crucial for manipulating the collective responses of nanoparticle arrays, which is also useful for practical applications. Herein, we design an array structure composed of L-shaped nanoantennas. Furthermore, we investigate the optical response caused by the coupling between the Rayleigh anomaly and bonding/antibonding modes. We find that the two kinds of surface-lattice resonances can be excited simultaneously in extinction spectra. Calculation results reveal that the bonding/antibonding modes can be used to couple with Rayleigh anomaly, thereby leading to the formation of orthogonal and parallel surface-lattice resonances. These properties make asymmetric nanoparticle arrays become promising platforms for designing micro-nano photonic devices.