In this work, we investigate the transmission sum rate as well as the secrecy sum rate of indoor visible light communication (VLC) networks for mobile devices with the power domain non-orthogonal multiple access (NOMA) transmission, where multiple legitimate users are equipped with photodiodes (PDs). We introduce a body blockage model of the legitimate users as well as the eavesdropper to focus on the case where the communications from transmitting light-emitting diodes (LEDs) to receiving devices are blocked by the bodies of receiving users. Furthermore, in order to improve the secrecy without any knowledge of the channel state information (CSI) of the eavesdropper, a novel LED arrangement is introduced to reduce the overlapping area covered by LED units supporting different users. We also propose two LED operation strategies, called simple and smart LED linking, and evaluate their performance against the conventional broadcasting in terms of transmission sum rate and secrecy sum rate. Through computer simulations, the superiority of our proposed strategies is demonstrated.