In sectors such as finance and healthcare, where data governance is subject to rigorous regulatory requirements, the exchange and utilization of data are particularly challenging. Federated Learning (FL) has risen as a pioneering distributed machine learning paradigm that enables collaborative model training across multiple institutions while maintaining data decentralization. Despite its advantages, FL is vulnerable to adversarial threats, particularly poisoning attacks during model aggregation, a process typically managed by a central server. However, in these systems, neural network models still possess the capacity to inadvertently memorize and potentially expose individual training instances. This presents a significant privacy risk, as attackers could reconstruct private data by leveraging the information contained in the model itself. Existing solutions fall short of providing a viable, privacy-preserving BRFL system that is both completely secure against information leakage and computationally efficient. To address these concerns, we propose Lancelot, an innovative and computationally efficient BRFL framework that employs fully homomorphic encryption (FHE) to safeguard against malicious client activities while preserving data privacy. Our extensive testing, which includes medical imaging diagnostics and widely-used public image datasets, demonstrates that Lancelot significantly outperforms existing methods, offering more than a twenty-fold increase in processing speed, all while maintaining data privacy.