An extreme ultraviolet pump and visible-light probe transmission experiment in crystalline LiF, carried out at the Free Electron Laser facility FERMI, revealed an oscillating time dependence of the plasmon mode excited in the high-density high-temperature electron plasma. The effect is interpreted as a fingerprint of the electron-ion interaction: the ion motion, shaped by the electron dynamic screening, induces, in turn, electron density fluctuations that cause the oscillation of the plasmon frequency at the timescale of the ion dynamics. Fitting the high resolution transmission data with an RPA model for the temperature-dependent dielectric function, which includes electron self-energy and electron-ion coupling, confirms the interpretation of the time modulation of the plasmon mode.