Ring signatures have been extensively researched for Cloud-assisted Electronic Medical Records (EMRs) sharing, aiming to address the challenge of “medical information silos” while safeguarding the privacy of patients’ personal information and the security of EMRs. However, most existing EMRs sharing systems that utilize ring signatures are vulnerable to quantum attacks, posing a severe challenge for the e-health scenario. To alleviate this issue, some studies have been conducted on lattice-based ring signatures. Nevertheless, there still exist two challenges. Firstly, current schemes fail to verify if multiple EMRs come from the same signer, undermining e-health reliability. Additionally, adversaries can exploit weaknesses in the network security of signers’ secret keys to forge signatures. In this paper, we propose an efficient lattice-based linkable ring signature (LLRS) for EMRs sharing to ensure patient privacy through anonymity, EMRs security through unforgeability, and checking the linkability for multiple signatures. We then present an enhancement scheme, called FS-LLRS, to additionally offer forward security, ensuring the security of previous ring signatures even if the current key has been compromised. To achieve this, we introduce a binary tree structure to divide time periods and leverage lattice basis algorithms for one-way secret key evolution, allowing users to update the secret keys periodically. Ultimately, we conduct a rigorous security analysis and compare our primitives with prior arts. In computational cost, the best performance of our LLRS and FS-LLRS schemes are just 0.17 and 0.34 times compared to others, respectively. Our LLRS scheme only incurs 0.08 times the communication overhead of others.