With the evolution of the Internet of Things, mutual sharing of information becomes easy among various smart devices across the globe. In such an environment, smart healthcare also needs to be expedited with an aim to provide remote diagnosis to patients located across the globe. However, as the sensitive information about a patient travels using an open channel (i.e., the Internet), there are chances of misusing this information. Hence, there is a requirement for a strong crypto mechanism for securely processing smart healthcare data. Most of the solutions reported in the literature use heavy computation-based solutions for providing security to smart healthcare data, which may not be suitable in view of less resources for modern smart devices. In this article, we propose a novel lattice-based secure cryptosystem for smart healthcare (LSCSH) in future smart cities. LSCSH uses a lightweight key exchange and an authentication mechanism at several stages. The proposed scheme has been evaluated with respect to the communication and computation costs in comparison to the other competitive schemes. The results obtained prove the efficacy of the proposed scheme in comparison to the existing schemes.