Lower hybrid waves are investigated at the magnetosheath separatrix region in asymmetric guide field reconnection by using the Magnetospheric Multiscale (MMS) mission. Three of the four MMS spacecraft observe clear wave activities around the lower hybrid frequency across the magnetosheath separatrix, where a density gradient is present. The observed waves are consistent with generation by the lower hybrid drift instability. The characteristic properties of these waves include the following: (1) the waves propagate toward the x-line in the spacecraft frame due to the large out-of-plane magnetic field, which is in the same direction of the diamagnetic drift of the x-line; (2) the wave potential is about 20% of the electron temperature. These drift waves effectively produce cross-field particle diffusion, enabling the transport of magnetosheath electrons into the exhaust region. At last, we suggest that the lower hybrid waves at the magnetosheath separatrix region represent some unique features of asymmetric guide field reconnection, which is different from that widely observed at the magnetospheric side of magnetopause reconnection. Plain Language Summary Magnetic reconnection is a fundamental process of explosive energy conversion in space, and one important unresolved issue during this process is how plasma waves impact the magnetic reconnection. Different types of waves have been found and investigated during reconnection, including kinetic Alfven waves, lower hybrid waves, whistler waves, upper hybrid waves, and parallel electrostatic waves. Among these waves, lower hybrid waves, taken as a basic feature of 3-D asymmetric reconnection, are frequently observed at the magnetospheric side. In this study, we present new observations from the Magnetospheric Multiscale (MMS) mission, showing that the lower hybrid waves can also be found at the magnetosheath separatrix in asymmetric guide field reconnection, which enable the cross-field particle diffusion from the magnetosheath to the exhaust. These results can help deepen our understanding of the roles of plasma waves in reconnection.