The Internet of Health Things (IoHT), which is an extension of the Internet of Things (IoT) in healthcare, has provided a new type of telemedicine approach. In IoHT, wearable sensors are used to collect patient health data, and information is transmitted remotely to doctors who can develop accurate treatment plans and provide timely telemedicine services to patients. However, patient health data are transmitted over a public channel, which means that the privacy and medical data of patients are at significant risk of leakage and can be confronted by serious security problems. We proposed a lightweight authentication protocol known as LAP-IoHT for IoHT environments to overcome the various threats that are currently faced by IoHT. We verified the security of LAP-IoHT using a Real-or-Random model and demonstrated its significant performance advantage by conducting a comparative analysis with other similar protocols for a better adaptation to the IoHT environment.