<p>IoT technology has fundamentally reshaped modern healthcare, offering capabilities such as uninterrupted patient monitoring, live data acquisition, and data-driven clinical decision-making. IoT-driven smart healthcare platforms support remote health tracking, timely identification of diseases, and rapid emergency interventions, all while cutting down on unnecessary hospital admissions and boosting overall care delivery. That said, rolling out IoT infrastructure at scale in healthcare settings brings with it a host of serious concerns—particularly around data security, patient privacy, system interoperability, and scalability. Handling sensitive patient information—including clinical records, physiological readings, and medical histories—demands the utmost care. Keeping such data out of unauthorized hands is fundamental to upholding patient confidentiality and trust. Classical cryptographic schemes, grounded in hard mathematical problems such as RSA and DLP, are now known to be susceptible to quantum-era attacks, rendering them insufficient for long-term security. In response, lattice-based cryptographic techniques have emerged as a compelling path forward for secure authentication and key exchange, offering robust resistance against quantum adversaries. Nevertheless, constructing a three-party, password-authenticated protocol that is both quantum-resilient and lightweight enough for constrained IoT hardware remains a genuinely difficult engineering challenge. In this work, we present a quantum-safe authenticated key agreement protocol for three parties, grounded in the ring learning with errors (RLWE) hardness assumption—a well-established variant of lattice-based cryptography. Unlike hybrid or partially post-quantum healthcare authentication schemes, the proposed protocol is fully lattice-based and formally modeled under the CK adversarial framework, providing explicit anonymity and unlinkability guarantees in a three-party IoT healthcare setting. The proposed protocol assisted with Fault-Tolerant is designed to resist impersonation, password guessing, and other common threats, while also enabling anonymous communication between two parties through a server. This protocol supports direct authenticated communication between user and multi-specialty doctor where user no need to communicate with server. The hospital have a dedicated server to facilitate doctor of various departments ( e.g. Cardiology, Neurology, Nephrology, Gastroenterology, Rheumatology etc ) within their organization that helps to give immediate response from doctor to user. The protocol achieves efficiency through the use of simple algebraic operations, specifically polynomial addition and multiplication, within the framework of lattice-based cryptography. We have also analyzed both computation and communication aspects of the proposed protocol, and found it suitable for healthcare applications. A comprehensive security comparison and performance analysis highlight the effectiveness and practicality of our proposed scheme, demonstrating its advantages over existing alternatives in real-world applications.</p>