Modern societies increasingly rely on interconnected devices and individuals for information exchange and monitoring. In this manner, drones, as flying smart nodes in the wireless network ecosystem, facilitate diverse applications, such as industrial, civilian, and disaster response operations. However, the widespread adoption of drone networks introduces significant challenges regarding interoperability, privacy, and security. Advances in quantum computing exacerbate these issues by rendering classical cryptographic measures inadequate, necessitating the adoption of quantum-safe approaches. Existing solutions fail to address all potential threats or lack post-quantum security. This work sets out to propose a robust lattice-based authentication and communication protocol for drone networks, addressing these challenges. The protocol integrates dynamic credentials, timestamps, multi-factor authentication, and context information to enhance security. The scheme's security is analyzed using the DY and BPR models and formally verified via the AVISPA tool. Performance evaluations and comparisons with existing solutions demonstrate the protocol's functionality, showcasing a reasonable trade-off between security and performance. By leveraging modern cryptographic techniques, the proposed scheme ensures reliable and robust drone operations, effectively mitigating various attacks beyond session establishment while safeguarding privacy, and supporting dynamic network events.