In this study, responses of Lamb waves to a bias electric field in a nanoplate with the consideration of piezoelectricity, flexoelectricity, and strain gradient elasticity are investigated. First, governing equations and boundary conditions of acoustic waves propagating in bias fields are derived. Then, dispersion equations under a bias electric field are obtained and solved numerically. Numerical solutions indicate that flexoelectricity can enhance the response of Lamb waves to external bias electric fields. It is also found that the competition between flexoelectricity and strain gradient elasticity leads to a complex variation of the voltage sensitivity with respect to the wavelength and frequency of Lamb waves. Our work may provide a way of resolving the contradiction between high sensitivity and miniaturization in the conventional voltage sensors based on surface acoustic waves. The theoretical results can guide a new design of voltage sensors with high sensitivity.