Medical Internet of Things (IoMT) is the next frontier in the digital revolution and is utilized in healthcare. In this context, IoT enables individuals to remotely manage their essential activities with minimal interaction. However, the limitations of network resources and the challenges of establishing a secure channel, as well as sharing and collecting sensitive information through an insecure public channel, pose security challenges for the medical IoT. This paper presents a lightweight multi-factor authentication and anonymous user authentication scheme to access real-time data in a blockchain-based environment. The scheme utilizes an insecure channel called L2AI. L2AI ensures security and efficiency while enhancing user anonymity through the use of pseudo-identity and dynamic indexing. The proposed method supports highly scalable systems with an efficient user registration process, allowing authenticated users to access both existing and newly added system entities without additional processes. Although the scheme is primarily designed for large systems, such as health infrastructure, it is also suitable for resource-constrained devices. The scheme relies on one-way cryptographic hashing functions and bitwise XOR operations. Additionally, a fuzzy mining algorithm is employed on the user side to verify the user's biometric information. L2AI adopts the "Real-Or-Random (ROR)" model for security proof and employs BAN logic for proof of authenticity. Formal security verification is conducted using the "Automatic Validation of Internet Security Protocols and Programs" (Proverif) tool, complemented by informal security analysis demonstrating the proper functionality of L2AI.