Privacy-preserving blockchain systems in regulated financial environments must simultaneously satisfy transaction confidentiality and regulatory compliance requirements. Existing schemes predominantly rely on elliptic curve cryptography, rendering them vulnerable to Harvest Now, Decrypt Later (HNDL) attacks posed by quantum computing advances. This paper proposes L-HCPM (Lattice-based Hybrid Cryptographic Protocol Model), a privacy-preserving blockchain protocol based on lattice cryptography that achieves both post-quantum security and regulatory auditability. The core contribution is the LT-Share (Lattice Trapdoor Shared Randomness) mechanism, which leverages GPV08/MP12 lattice trapdoor sampling to generate shared randomness between users and regulators, enabling regulators to independently decrypt transactions without user cooperation. To address the non-reproducibility of Peikert randomized sampling under the UTXO model, we introduce an off-chain caching architecture to ensure sampling consistency. We further extend the Universal Composability (UC) framework by introducing a hybrid adversary model, formally proving the secure composability of quantum-secure and classical-secure components. Experimental evaluation based on a complete prototype system demonstrates that post-quantum cryptographic overhead accounts for only 0.17% of end-to-end latency, with Gas consumption ranging from 337 K to 686 K, and regulatory decryption achieving 100% success rate, validating the practical feasibility of post-quantum security upgrades.