In recent years, the linkable ring signature schemes have emerged continuously, but they always face the challenge of key escrow, where the malicious KGC poses the risk of leaking user keys. To address the issue of key escrow in identity-based linkable ring signature, the certificateless cryptosystem is integrated into lattice-based linkable ring signatures, and this lattice-based certificateless linkable ring signature scheme is designed based on the small integer solution (SIS) problem, which is a known NP-hard problem on lattices. In the random oracle model, this scheme can assure three key properties—user identity anonymity, signature unforgeability, and linkability—against both types of adversaries (external users and malicious KGC). Compared with existing lattice-based certificateless ring signature schemes, the scheme has a more complete security proof. While satisfying the linkability (added linkable tags), the time for signature generation and verification has been reduced by approximately 20%. Furthermore, the certificateless lattice based linkable ring signature is applied to blockchain electronic transactions, which not only solves key escrow and complex certificate management, but also meets the lightweight needs of blockchain system.