While ideal lattice models have been widely used to study giant-atom systems, fabrication-induced imperfections inevitably introduce disorder in realistic platforms. Here, we study the non-Markovian dynamics of a giant atom coupled to a discrete photonic lattice with static on-site frequency disorder. Using time-domain and spectral analyses, we find that the overall population-decay envelope and global photon-transport patterns remain qualitatively robust within the explored disorder range, while the accumulated non-Markovianity shows a modest overall increasing trend with disorder. We characterize the information backflow using a cumulative normalized geometrical non-Markovianity measure and show that the coupling-point separation primarily determines the feedback delay timescale, whereas the disorder strength provides a weaker modulation of the accumulated backflow. The overall spectral structure remains qualitatively similar in the ordered and disordered lattices, with only small disorder-induced shifts in some of the out-of-band branches. The representative real-space profiles of the selected out-of-band states also remain qualitatively similar, with only minor quantitative changes. These observations are consistent with the relatively small disorder-induced changes in the delayed-revival dynamics. Our results provide a disorder-aware description of non-Markovian giant-atom dynamics in structured reservoirs.

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• Quantum description of light-matter interaction
• Quantum optics
• Waveguide arrays
• Disordered systems
• Markovian processes