Wireless networking on a 24/7 basis leads to significant energy consumption and carbon emissions in hospitals. This paper discusses the possibility of implementing Light Fidelity (LiFi) as an energy-saving, greener version of the conventional Wi-Fi in hospitals. We perform the comparison on the energy consumption of both Wi-Fi and LiFi applications based on a case study of a normal hospital, including 100 modules of the network. As demonstrated in our calculations, LiFi uses only about 4.8 kWh a day, representing savings of nearly three-quarters (75%) of the energy (19.2 kWh a day) consumed by Wi-Fi. This power consumption saves an estimated 13.25 kg (or nearly 75% more as compared to Wi-Fi) of CO2 emissions daily. Besides these environmental advantages, LiFi has minimal electromagnetic interference, more data security, and has the potential to generate less electronic waste, which comes in handy in such sensitive hospital environments. These results lead to the conclusion that it is possible to replace Wi-Fi with LiFi at a relatively low cost without reducing network capacity, energy costs, or the carbon footprint of hospital networks, while also increasing the level of data protection and network security. A sensitivity analysis further confirms that these savings remain substantial across a range of realistic power consumption values, making the conclusion robust rather than dependent on a single assumed case. All in all, our findings provide a strong operational imperative for hospitals to adopt LiFi as a major step toward greener, more sustainable health infrastructures.