Estimating surface normals in airborne LiDAR point clouds is a critical step in mesh reconstruction and other downstream tasks such as semantic segmentation. Conventional methods often rely on local surface fitting combined with heuristic orientation strategies, which require careful parameter tuning and often yield inconsistent results, either globally, as in Minimum-Spanning-Trees, or locally on vertical structures, as in global axis-based orientation. In this work, we present two deep learning approaches based on a Point Transformer V3 encoder architecture for normal estimation in unstructured airborne LiDAR point clouds. The first approach treats normal orientation as a binary classification, flipping pre-computed normals to achieve consistent orientations. The second approach directly predicts the full normal vector. Both approaches estimate the results for all points simultaneously, which enables efficient processing of large-scale point clouds. Since no aerial LiDAR dataset provides reference normals for direct evaluation, we employ an indirect evaluation strategy based on Poisson surface reconstruction to assess the quality of the meshes generated from the estimated normals. Our method for full normal estimation outperforms the strongest baseline by up to 2 percentage points in terms of F1-Score, as shown by experiments with three reference LiDAR datasets: UseGeo, Hessigheim 3D, and our holdout dataset JB3D. However, our qualitative results also highlight the limitations of this approach. Since the training data consists of point clouds derived from photogrammetric point clouds and point clouds sampled from textured meshes, our approach for full normal vector estimation tends to result in noticeable smoothed edges.