LiDAR-based perception in autonomous systems is constrained by fixed vertical beam resolution and further compromised by beam dropout resulting from environmental occlusions. This paper introduces SuperiorGAT, a graph attention-based framework designed to reconstruct missing elevation information in sparse LiDAR point clouds. By modeling LiDAR scans as beam-aware graphs and incorporating gated residual fusion with feed-forward refinement, SuperiorGAT enables accurate reconstruction without increasing network depth. To evaluate performance, structured beam dropout is simulated by removing every fourth vertical scanning beam. Extensive experiments across diverse KITTI environments, including Person, Road, Campus, and City sequences, demonstrate that SuperiorGAT consistently achieves lower reconstruction error and improved geometric consistency compared to PointNet-based models and deeper GAT baselines. Qualitative X-Z projections further confirm the model's ability to preserve structural integrity with minimal vertical distortion. These results suggest that architectural refinement offers a computationally efficient method for improving LiDAR resolution without requiring additional sensor hardware.