With the increasing number and enhanced capabilities of IoT devices in smart buildings, these devices are evolving beyond basic data collection and control to actively participate in deep learning tasks. Federated Learning (FL), as a decentralized learning paradigm, is well-suited for such scenarios. However, the limited computational and communication resources of IoT devices present significant challenges. While existing research has extensively explored efficiency improvements in Horizontal FL, these techniques cannot be directly applied to Vertical FL due to fundamental differences in data partitioning and model structure. To address this gap, we propose a Lightweight Vertical Federated Learning (LVFL) framework that jointly optimizes computational and communication efficiency. Our approach introduces two distinct lightweighting strategies: one for reducing the complexity of the feature model to improve local computation, and another for compressing feature embeddings to reduce communication overhead. Furthermore, we derive a convergence bound for the proposed LVFL algorithm that explicitly incorporates both computation and communication lightweighting ratios. Experimental results on an image classification task demonstrate that LVFL effectively mitigates resource demands while maintaining competitive learning performance.