We present a detailed study of fluctuations in a laboratory current sheet undergoing magnetic reconnection. The measurements reveal the presence of lower-hybrid-frequency-range fluctuations on the edge of current sheets produced in the magnetic reconnection experiment (MRX). The measured fluctuation characteristics are consistent with theoretical predictions for the lower-hybrid drift instability (LHDI). Our observations suggest that the LHDI turbulence alone cannot explain the observed fast reconnection rate in MRX.