This study utilizes the mold flow analysis technique of the injection compression molding (ICM) process, combined with the Taguchi–gray relational analysis (GRA), for process optimization analysis on the roundness of the lens holes and the flatness of the lens mount in a 4 × 4 planar multilens array mount. After manufacturing simulation analysis, the eccentricity and tilt information of the lens mount was further evaluated optically through spot diagram analysis upon inserting the same glass lenses. The results showed a positive correlation trend between roundness and flatness in structural deformation analysis, indicating that improving the overall flatness of the lens mount can enhance the roundness of the lens holes. In optical analysis, better improvements in the lens tilt angle were achieved through GRA. In conclusion, aiming to simultaneously improve the roundness of the lens holes and the overall flatness of the lens mount, the Taguchi–GRA method can achieve the optimization objectives. In terms of optical performance, by optimizing for roundness, it is possible not only to reduce the diameter of the light spot but also to simultaneously reduce the offset displacement of the light spot center on the screen. The method proposed in this paper can serve as an analytical model for the design and fabrication of plastic multilens mount.