Smart grid (SG) is a modernized power grid that uses information and communication technologies for bidirectional flow of information between the power utilities and the consumers. Nowadays, the focus of SG has shifted towards intelligent processing and control of various operations in order to provide high quality of experience to the end users domain (consumers, smart devices, utility, etc). Therefore, in near future, for smooth execution of various operations in SG, high volume of data is expected to move across different inter-connected smart devices. So, to handle this challenge, a self-configurable network technology known as software-defined networking (SDN)that provides faster and dynamic forwarding of data through adaptable flow-table management is a viable solution. However, in SDN- enabled SG systems, security and privacy are major challenges that need to be handled effectively. So, in this paper, a lattice-based cryptosystem for secure communication in SG environment, called LaCSys, is presented which works in three phases. In first phase, a secure authentication between all the network communication entities based on lattice based key exchange scheme is designed using a third party auditor (TPA). In second phase, a lightweight lattice-based public-key encryption scheme is designed to provide data confidentiality and integrity. In last phase, a temporary key-based scheme for detection of suspicious activity is designed. The proposed crytosystem is evaluated and compared with existing scheme in order to prove its effectiveness.