A drone is an unmanned aerial vehicle, which is deployed in a particular Fly Zone (FZ), and used to collect crucial information from its surrounding environment to be transmitted to the server for further processing. Generally, a Mobile User (MU) is required to access the real-time information collected by the drone stationed in a specific FZ securely. Therefore, to ensure secure and reliable communications an Authenticated Key Exchange (AKE) protocol is imperative to the Internet of Drone (IoD) environment. An AKE scheme ensures only authentic MU to access IoD network resources. Upon successful authentication, MU and drone can set up a secret session key for secure communication in the future. This paper presents a novel Lightweight AKE Protocol for IoD Environment (LAKE-IoD), which first ensures the authenticity of MU and also renders session key establishment mechanism between MU and drone with the help of a server. LAKE-IoD is an AKE protocol, which is based on an authenticated encryption scheme AEGIS, hash function, and bit-wise XOR operation. Meticulous formal security verification by employing a software tool known as Scyther and informal security analysis demonstrates that LAKE-IoD is protected against different well-known active and passive security attacks. Additionally, Burrows-Abadi-Needham logic is applied to verify the logical completeness of LAKE-IoD. Furthermore, a comparison of LAKE-IoD with the related schemes shows that LAKE-IoD incurs less communication, computational and storage overhead.