Availability of datasets is a strong driver for research on 3D semantic understanding, and whilst obtaining unlabeled 3D point cloud data is straightforward, manually annotating this data with semantic labels is time-consuming and costly. Recently, Vision Foundation Models (VFMs) enable open-set semantic segmentation on camera images, potentially aiding automatic labeling. However, VFMs for 3D data have been limited to adaptations of 2D models, which can introduce inconsistencies to 3D labels. This work introduces Label Any Pointcloud (LeAP), leveraging 2D VFMs to automatically label multi-frame 3D data with any set of classes in any kind of application whilst ensuring label consistency. Using a Bayesian update, point labels are combined into voxels to improve spatio-temporal consistency. A novel 3D Consistency Network (3D-CN) exploits 3D information to further improve label quality. Through various experiments, we show that our method can generate high-quality 3D semantic labels across diverse fields without any manual labeling. Further, models adapted to new domains using our labels show a significant mIoU increase in semantic segmentation tasks.