High resolution crop type maps are an important tool for improving food security, and remote sensing is increasingly used to create such maps in regions that possess ground truth labels for model training. However, these labels are absent in many regions, and models trained in other regions on typical satellite features, such as those from optical sensors, often exhibit low performance when transferred. Here we explore the use of NASA's Global Ecosystem Dynamics Investigation (GEDI) spaceborne lidar instrument, combined with Sentinel-2 optical data, for crop type mapping. Using data from three major cropped regions (in China, France, and the United States) we first demonstrate that GEDI energy profiles are capable of reliably distinguishing maize, a crop typically above 2m in height, from crops like rice and soybean that are shorter. We further show that these GEDI profiles provide much more invariant features across geographies compared to spectral and phenological features detected by passive optical sensors. GEDI is able to distinguish maize from other crops within each region with accuracies higher than 84\%, and able to transfer across regions with accuracies higher than 82\% compared to 64\% for transfer of optical features. Finally, we show that GEDI profiles can be used to generate training labels for models based on optical imagery from Sentinel-2, thereby enabling the creation of 10m wall-to-wall maps of tall versus short crops in label-scarce regions. As maize is the second most widely grown crop in the world and often the only tall crop grown within a landscape, we conclude that GEDI offers great promise for improving global crop type maps.