Attribute-based encryption is useful for one-to-many encrypted message sending. However, most attribute-based encryption schemes authorize and issue attributes to users by a single authority. Such a scenario conflicts with practical requirements and may cause the key-escrow problem. Hence, decentralization of authority is a critical issue in attribute-based encryption. Besides, dynamic membership management is another important issue in attribute-based encryption. With dynamic membership management, a system may update the user's attributes without affecting other users, making the system more flexible and practical. On the other hand, with the rapid development of quantum computers nowadays, encryption schemes based on traditional mathematical problems are at the risk of quantum attacks. Among the existing quantumresistant mathematical architectures, lattice-based cryptography is the most widely studied. Thus, we propose a multi-authority attribute-based encryption scheme with dynamic membership from lattices to solve the above problems. Moreover, we also formally prove the security of the proposed scheme under the decisional learning with errors assumption.