In this paper, we consider a light fidelity (LiFi)-enabled bidirectional Internet of Things (IoT) communication system, where visible light and infrared light are used in the downlink and uplink, respectively. In order to improve the energy efficiency (EE) of the bidirectional LiFi-IoT system, non-orthogonal multiple access (NOMA) with a quality-of-service (QoS)-guaranteed optimal power allocation (OPA) strategy is applied to maximize the EE of the system. We derive a closed-form OPA set based on the identification of the optimal decoding orders in both downlink and uplink channels, which can enable low-complexity power allocation. Moreover, we propose an adaptive channel and QoS-based user pairing approach by jointly considering users channel gains and QoS requirements. We further analyze the EE of the bidirectional LiFi-IoT system and the user outage probabilities (UOPs) of both downlink and uplink channels of the system. Extensive analytical and simulation results demonstrate the superiority of NOMA with OPA in comparison to orthogonal multiple access (OMA) and NOMA with typical channel-based power allocation strategies. It is also shown that the proposed adaptive channel and QoS-based user pairing approach greatly outperforms individual channel/QoS-based approaches, especially when users have diverse QoS requirements.