Conventional cryptographic constructions have to meet the challenge of the quick development of quantum computing, and they require the creation of efficient constructions resistant to quantum attack. In this paper, the authors suggest a hybrid cryptographic model that combines lattice-based hardness assumptions, such as Learning with Errors (LWE) with graph theoretical and combinatorial structures to provide greater security, efficiency and scalability. This framework is a hybrid of lattice trapdoor functions, expander graphs, and discrete optimization methods, aiming to enhance structural robustness against classical and quantum attackers. The performance is compared with the conventional methods of RSA/ECC and lattice and graph-based cryptographic methods. The results reported in this work shows that, the proposed hybrid framework provides the security level of 256 bits and quantum attack resistance as 96.8%, whereas the lattice-based approach provides 82.4%. Moreover, the hybrid construction has the key generation time 21.1ms, encryption time 14.1ms and throughput of 183Mbps. These values represent a decrease of 14.92% for the key generation time, 10.19% for the encryption time and 27.96% for the memory usage when compared to the baseline which is based on lattices. These results indicate that a combination of complementary discrete mathematical models could be a potential way to design efficient, scalable post-quantum cryptographic systems.