Quantum-proof authentication is essential for vehicular communications as the threat of quantum computing attacks on traditional encryption methods grows. Several lattice-based authentication protocols have recently been developed to help with this issue, but they come with hefty storage and communication overheads. Most of them also fail to provide strong anonymity for vehicles and edge nodes and can not support authentication for vehicles from multiple domains. This study presents a new lattice-based authentication protocol for vehicular communications that addresses limitations of previous methods and offers advanced security features such as anonymity, and unlinkability. The protocol utilizes a distributed ledger to store public keys, making the system more secure, tamper-proof, and efficient for key revocation in large networks. Additionally, it allows for a multi-domain authentication system for vehicular communication with improved security and flexibility. The proposed protocol's security is evaluated both formally and informally to demonstrate its resistance against the well-known attacks. Additionally, the performance analysis indicates that the proposed protocol surpasses current protocols and is suitable for vehicular communications.