We demonstrate the possibility of the existence and propagation of dust acoustic solitons in the dusty plasma of the lunar exosphere, which contains, in addition to electrons and ions of the solar wind and photoelectrons from its surface, charged dust particles, as well as photoelectrons emitting from the surfaces of these particles. Soliton solutions are found and the ranges of possible velocities and amplitudes of such solitons are determined depending on the height above the lunar surface for different subsolar angles.