LiDAR-captured point clouds are often considered the gold standard in active 3D reconstruction. While their accuracy is exceptional in flat regions, the capturing is susceptible to miss small geometric structures and may fail with dark, absorbent materials. Alternatively, capturing multiple photos of the scene and applying 3D photogrammetry can infer these details as they often represent feature-rich regions. However, the accuracy of LiDAR for featureless regions is rarely reached. Therefore, we suggest combining the strengths of LiDAR and camera-based capture by introducing SurfFill: a Gaussian surfel-based LiDAR completion scheme. We analyze LiDAR capturings and attribute LiDAR beam divergence as a main factor for artifacts, manifesting mostly at thin structures and edges. We use this insight to introduce an ambiguity heuristic for completed scans by evaluating the change in density in the point cloud. This allows us to identify points close to missed areas, which we can then use to grow additional points from to complete the scan. For this point growing, we constrain Gaussian surfel reconstruction to focus optimization and densification on these ambiguous areas. Finally, Gaussian primitives of the reconstruction in ambiguous areas are extracted and sampled for points to complete the point cloud. To address the challenges of large-scale reconstruction, we extend this pipeline with a divide-and-conquer scheme for building-sized point cloud completion. We evaluate on the task of LiDAR point cloud completion of synthetic and real-world scenes and find that our method outperforms previous reconstruction methods.