Cellular-Vehicle-to-Everything (C-V2X) is featured as a heterogenous network, with the support of cellular based uplink/downlink transmissions and sidelink communications as well as network backhauling, where infringement on security can happen. Additionally, the developing quantum attack strikes the original NP-hard problems to be solvable in polynomial time complexity. Therefore, it is fatal to build a secure environment for vehicles to communicate in C-V2X. In this paper, we propose a key management scheme utilizing blockchain deployed at the base station for distributed storage and retrieval of vehicles' public keys. In the network, each vehicle is identified with a public-private key pair, upon which vehicular registration, authenticated key agreement and revocation rely. In particular, the lattice-based cryptography is applied to the distribution of the group key for broadcasting beacon messages and establishing session keys for a secure peer-to-peer (P2P) communication. Keys are updated as vehicles travel from one region to another and are revoked upon misbehavior detection. We analyzed the quantum resistance of our scheme theoretically and its conservation against certain attacks informally. Comparative analysis across computation, communication, storage and energy consumption demonstrates the characteristics of our scheme. Finally, the blockchain simulation demonstrates the scalability of our scheme.