Intelligent equipment fault diagnosis based on Federated Transfer Learning (FTL) attracts considerable attention from both academia and industry. It allows real-world industrial agents with limited samples to construct a fault diagnosis model without jeopardizing their raw data privacy. Existing approaches, however, can neither address the intense sample heterogeneity caused by different working conditions of practical agents, nor the extreme fault label scarcity, even zero, of newly deployed equipment. To address these issues, we present FedLED, the first unsupervised vertical FTL equipment fault diagnosis method, where knowledge of the unlabeled target domain is further exploited for effective unsupervised model transfer. Results of extensive experiments using data of real equipment monitoring demonstrate that FedLED obviously outperforms SOTA approaches in terms of both diagnosis accuracy (up to 4.13 times) and generality. We expect our work to inspire further study on label-free equipment fault diagnosis systematically enhanced by target domain knowledge.