Blockchain-enhanced Smart Grid has attracted a lot of attention from scholars in recent years, due to its excellent decentralization, anti-collusion and immutability. With the wide deployment of blockchain and the popularity of more accurate intelligent applications, its role in Smart Grid is becoming more and more irreplaceable. However, because of the threat of quantum computer, it still confronts the risk of privacy disclosure. In this article, we propose a novel and dynamic range query privacy-preserving scheme for blockchain-enhanced Smart Grid based on lattice. In this scheme, lattice-based homomorphic encryption algorithm is designed to resist the attack of quantum computer and realizes data aggregation to improve efficiency. In particular, this article designs a dynamic range query method with the aid of consortium blockchain by using proxy re-encryption. This method avoids the communication pressure caused by repeated data collection and improves the query efficiency and user experience. In addition, dynamic ciphertext and users update are considered, which further improves the flexibility and feasibility of the scheme. Last but not least, security analysis, exhaustive performance analysis and experiments show that our proposed scheme meets the requirements of dynamic, privacy, security and low computational cost.