The Internet of Things (IoT) is a new emerging system of interconnected devices that experiences significant growth in a wide variety of applications. The rising communication technologies for IoT are the Low Power Wide Area Networks (LPWANs) having long range, low cost and low power characteristics. In this context, an important part of the applications requires the mobility of the end devices with secure communications. In this paper, we consider the mobility management solutions in LPWAN networks and we investigate how they ensure security. We first review the basic IoT security requirements and the typical IoT protocol stack. We then focus on the existing mobility management solutions in LPWAN and we highlight the mobility related security issues by checking the attacks that can be performed in case of mobility. Furthermore, we evaluate the security in each mobility solution by checking the aforementioned attacks and we draw a comparison study.