<p>Certificateless linearly homomorphic signature (CLHS) is a novel cryptographic tool that enables the generation of verifiable signatures for linearly computed data without requiring a trusted third party to issue digital certificates, integrating both identity authentication and data integrity protection. The security of most of these schemes is based on classical number-theoretic problems, which are easily broken by quantum computing techniques. In this paper, we propose a lattice-based CLHS scheme and prove that it satisfies signature correctness, combined signature correctness, weak context hiding, and unforgeability. In comparison with the other three schemes of the same type, our scheme eliminates key escrow and defends against attacks from corrupted Key Generation Center (KGC) without significantly increasing the length of keys and signatures. Furthermore, we show that the design of Dong et al.’s scheme contains fundamental flaws based on our analysis.</p>