We numerically investigate electron quantum transport in 2D van der Waals tunnel field-effect-transistors in the presence of lateral momentum mismatch induced by lattice mismatch or rotational misalignment between the two-dimensional layers. We show that a small momentum mismatch induces a threshold voltage shift without altering the subthreshold swing. On the contrary, a large momentum mismatch produces significant potential variations and ON-current reduction. Short-range scattering, such as that due to phonons or system edges, enables momentum variations, thus enhancing interlayer tunneling. The coupling of electrons with acoustic phonons is shown to increase the ON current without affecting the subthreshold swing. In the case of optical phonons, the ON-current increase is accompanied by a subthreshold swing degradation due to the inelastic nature of the scattering.