We study the ionization of a hydrogenic target by the impact of moderate energy electrons and in the presence of a laser field. This process, generally referred to as the laser-assisted (e,2e), is treated non-relativistically as follows: we evaluate the S-matrix elements using Volkov and Coulomb-Volkov wavefunctions for describing respectively the continuum states of the scattered and the ejected elecrons. The dressed state of the target is described by a time-dependent wavefunction derived from a perturbation treatment (of the laser field). With the aid of numerical results we explore the dependences of the fully differential cross sections on the laser field properties such as the strength, the frequency and the polarization direction, as well as on the continuum electron energies and their emission angles. Furthermore, we asses the interplay between the laser influence and the role of scattering from the residual ion by comparing the cross-sections from (one-electron) ionic targets and varying in the charge state of the residual ion.