The ever-increasing demand for high data-rate applications and the proliferation of connected devices pose several theoretical and technological challenges for the fifth generation (5G) networks and beyond. Among others, this includes the spectrum scarcity and massive connectivity of devices, particularly in the context of the Internet of Things (IoT) ecosystem. In this respect, visible light communication (VLC) has recently emerged as a potential solution for these challenges, particularly in scenarios relating to indoor communications. Additionally, non-orthogonal multiple access (NOMA) for VLC has been envisioned to address some of the key challenges in the next generation wireless networks. However, in realistic environments, it has been shown that VLC systems suffer from additive optical interference due to ambient light, and user-mobility which cause detrimental outages and overall degraded data rates. Motivated by this, in this work, we first derive the statistics of the incurred additive interference, and then analyze the rate of the considered NOMA-VLC channel. An analytical expression is subsequently derived for the rate of NOMA-VLC systems with ambient light and user-mobility, followed by the formulation of a power-allocation technique for the underlying scenario, which has been shown to outperform classical gain-ratio power allocation in terms of achievable rate. The obtained analytical results are corroborated with computer simulations for various realistic VLC scenarios of interest, which lead to useful insights of theoretical and practical interest. For example, it is shown that, in a NOMA-enabled VLC system, the maximum rate at which information can be transmitted over a static VLC communication channel with ambient light asymptotically converges to the Shannon Hartley capacity formula.