Tungsten (W) sputtering from the guard limiter of lower hybrid wave (LHW) antenna is an impurity source in EAST. While theoretical studies suggest that the super-thermal electrons generated via plasma-LHW interactions contribute to the W production, the role of these electrons in W sputtering from the guard limiter remains unresolved—particularly when optimizing edge density for long-pulse operation. To address this, we developed a model with realistic incident power spectra to study the influence of the acceleration of electrons by LHW on the sheath properties. It is found that both the edge density and the LHW power determine the velocity distribution function of super-thermal electrons. Consequently, for the low edge density, the super-thermal electrons are insufficient to significantly alter the sheath structure, causing the sheath potential to retain its typical dependence on the electron temperature. In contrast, for the high edge density, when the super-thermal electrons dominate the sheath dynamics, the sheath potential near the guard limiter is substantially enhanced. Its magnitude scales monotonically with LHW power but seems weak dependence on the electron temperature. The resulting strong sheath potential dramatically increases the W sputtering yield from the guard limiter of LHW antenna under multi-species ion bombardment, potentially triggering confinement degradation. By clarifying the role of edge density in W sputtering from the guard limiter of LHW antenna, these results provide a candidate approach to mitigate W production on EAST during lower hybrid current drive operation.