The influence of nonthermal Lorentzian wake-field on the electron-dust grain collision is investigated in complex dusty plasmas. The Eikonal method and the effective interaction potential are applied to obtain the Eikonal scattering phase shift, the differential Eikonal collision cross section, and the total Eikonal collision cross section as functions of the collision energy, the impact parameter, the Mach number, and the spectral index of Lorentzian plasma. It is found that the nonthermal effect enhances the Eikonal scattering phase shift and, however, suppresses the Eikonal collision cross section for the electron-dust grain in Lorentzian complex dusty plasmas. It is also found that the Eikonal scattering phase shift decreases with increasing Mach number and spectral index. In addition, the Eikonal collision cross section increases with an increase of the spectral index and Mach number in Lorentzian complex dusty plasmas.