The integration of smart medical technology has revolutionized personal health management, with devices like smartwatches and smartphones facilitating efficient data collection and analysis. However, the exponential growth in medical data has heightened privacy concerns, underscoring the need for a robust and secure transmission system. Traditional encryption, while effective, is limited by its resource-intensive nature, hindering its application in IoT devices. Our research delves into the application of compressed sensing for medical image privacy, addressing challenges such as high resource consumption, security vulnerabilities, and the need for robust watermarking. We have designed the Lightweight Quantum-resistant Medical Image Transmission (LQRMIT) model, which combines a 3D chaotic system with the Learning With Errors (LWE) theory, offering a key space of up to$2^{700}$, significantly enhancing security. Additionally, we have designed a watermark embedding algorithm compatible with compressed sensing, which ensures high invisibility and high-quality watermark extraction. The model also employs a meaningful image hiding strategy within encrypted transmissions to improve stealth. Extensive experimental and theoretical analysis has validated the effectiveness of our solution, providing a promising approach for secure and efficient medical image transmission in the digital medical era.