The medical analytics that protect privacy has gained urgency as the amount of sensitive healthcare information has been increasing rapidly and regulatory restrictions are imposed. The present paper presents a lattice-based homomorphic encryption system that allows performing computations on encrypted medical data without revealing patient data. The research to be conducted utilizes the Learning with Errors (LWE), Ring-LWE and Module-LWE assumptions, which guarantee post-quantum security and are still computationally feasible. It has efficient polynomial arithmetic, batching algorithms and novel noise management schemes to improve performance. Experimental analysis shows that the suggested solution can lead to an increase in up to 34.8% of the computation efficiency and a decrease in latency by 41.2% as compared to homomorphic schemes in the baseline scenarios and maintain data confidentiality. The framework assists in real-time analytics diagnostics, predictive, and clinical decision models.