Smart metering infrastructure (SMI) is the core component of the smart grid (SG) which enables two-way communication between consumers and utility companies to control, monitor, and manage the energy consumption data. Despite their salient features, SMIs equipped with information and communication technology are associated with new threats due to their dependency on public communication networks. Therefore, the security of SMI communications raises the need for robust authentication and key agreement primitives that can satisfy the security requirements of the SG. Thus, in order to realize the aforementioned issues, this paper introduces a lightweight and secure authentication protocol, "LiSA", primarily to secure SMIs in SG setups. The protocol employs Elliptic Curve Cryptography at its core to provide various security features such as mutual authentication, anonymity, replay protection, session key security, and resistance against various attacks. Precisely, LiSA exploits the hardness of the Elliptic Curve Qu Vanstone (EVQV) certificate mechanism along with Elliptic Curve Diffie Hellman Problem (ECDHP) and Elliptic Curve Discrete Logarithm Problem (ECDLP). Additionally, LiSA is designed to provide the highest level of security relative to the existing schemes with least computational and communicational overheads. For instance, LiSA incurred barely 11.826 ms and 0.992 ms for executing different passes across the smart meter and the service providers. Further, it required a total of 544 bits for message transmission during each session.