We systematically studied the lasing characteristics in photonic polycrystalline and amorphous structures. 2D arrays of air holes were fabricated in a GaAs membrane. InAs quantum dots embedded in the membrane provide gain for lasing under optical pumping. The lasing modes are spatially localized, and blue shift as the structural order becomes short ranged. Our three-dimensional numerical simulations reveal that the out-of-plane leakage of the lasing mode dominates over the in-plane leakage. The lasing modes in a photonic polycrystalline move away from the center frequency of the photonic band gap to reduce the out-of-plane leakage. In a photonic amorphous structure, the short-range order improves optical confinement and enhances the quality factor of resonances. Understanding the behavior of photonic polycrystalline laser and amorphous laser opens the possibility of controlling lasing characteristic by varying the degree of structural order.