Hybrid Li-Fi/Wi-Fi networks are increasingly adopted for high-capacity indoor connectivity to mitigate RF spectrum congestion. However, Li-Fi performance is highly sensitive to user mobility, device orientation, and blockage, which are often overlooked in hybrid designs. This letter proposes OAM-LiFiNet, an orientation-aware, multi-AP hybrid Li-Fi/Wi-Fi framework with selective, sensor-assisted orientation control and mobility-aware link selection. Device orientation is triggered only when it provides measurable SINR or throughput gains, avoiding unnecessary adjustments. By integrating Random Waypoint mobility, blockage awareness, and interference-aware SINR evaluation, the proposed framework improves throughput stability and handover efficiency. Simulation results show up to 84% throughput improvement with fewer orientation adjustments compared to baseline hybrid schemes.