5G and beyond will occupy a big position in wireless communication future, because of the high end-user data rate over the Internet demand. Millimeter wave (mmWave) plays the major role as a 5G networks enabler. To overcome mmWave band propagation losses and increase its coverage area, beamforming training (BT) is typically used in conjunction with mmWave transmissions. IEEE 802.11ad standard defines an exhaustive search BT to find out the best transmit (TX)/receive (RX) beam identifications (IDs). Narrow, i.e., pencil, beams guarantee a high gain, i.e., a wide coverage area, but at the expense of very high setup time due to the exhaustive searching process. Localization provides a promising solution for finding out the best mmWave beams within a small setup time. However, localization techniques having high localization errors compared with the coverage area of the sharp beams (e.g., 5 degrees) are not suitable for these scenarios. Motivated by the high publicity of light emitting diode (LED) lambs and their high accurate positioning (e.g., around 10 cm), a mmWave BT technique based on light fidelity (Li-Fi) multilateral positioning is proposed in this paper to work efficiently in mmWave sharp beam scenarios. Via mathematical and simulation analysis, the proposed mmWave BT achieves a few number of beam switchings with a comparable performance with the exhaustive search BT. Besides, it achieves a lower outage probability than that comes from using Wi-Fi Localization.