Light-fidelity (LiFi) is a fully-networked bidirectional optical wireless communication (OWC) that is considered a promising solution for high-speed indoor connectivity. Unlike in conventional radio frequency wireless systems, the OWC channel is not isotropic, meaning that the device orientation affects the channel gain significantly. However, due to the lack of proper channel models for LiFi systems, many studies have assumed that the receiver is vertically upward and randomly located within the coverage area, which is not a realistic assumption from a practical point of view. In this paper, novel realistic and measurement-based channel models for indoor LiFi systems are proposed. Precisely, the statistics of the channel gain are derived for the case of randomly oriented stationary and mobile LiFi receivers. For stationary users, two channel models are proposed, namely, the modified truncated Laplace (MTL) model and the modified Beta (MB) model. For LiFi users, two channel models are proposed, namely, the sum of modified truncated Gaussian (SMTG) model and the sum of modified Beta (SMB) model. Based on the derived models, the impact of random orientation and spatial distribution of LiFi users is investigated, where we show that the aforementioned factors can strongly affect the channel gain and system performance.