The security of lattice-based post-quantum cryptographic schemes depends fundamentally on the hardness of computational problems defined over structured algebraic lattices, including the shortest vector problem (SVP), the closest vector problem (CVP), and the learning with errors (LWE) problem. Accurately evaluating the concrete security level of deployed schemes requires solving or bounding these hard problems for specific lattice instances, a task that has historically relied on heuristic analysis using the Gaussian heuristic and the Hermite factor. This paper presents a novel Algebraic Lattice Decomposition (ALD) framework that integrates the LLL and BKZ basis reduction algorithms with a Transformer-LSTM hybrid artificial intelligence model to produce rapid, accurate, and mathematically rigorous security level estimates for cryptographic schemes. The ALD framework decomposes the cryptographic lattice into hierarchically structured sublattices using Gram-Schmidt orthogonalisation and algebraic norm analysis, extracting a high-dimensional feature vector that encodes the geometric and spectral properties of the reduced basis. The Transformer-LSTM model is trained on 84,000 lattice instances spanning eight NIST post-quantum candidate schemes including CRYSTALS-Kyber, NTRU, and CRYSTALS-Dilithium, learning to map lattice geometric invariants to security level estimates with a mean absolute error of 1.18 bits. Comprehensive evaluation demonstrates that the proposed framework achieves 97.84% classification accuracy for vulnerability categorization, AUC-ROC of 0.9921, and a 3.5× speedup over conventional BKZ-20 analysis for lattices of dimension n = 512.