There has been tremendous progress in manipulating electron and hole-spin states in quantum dots or quantum dot molecules (QDMs) with growth-direction (vertical) electric fields and optical excitations. However, the response of carriers in QDMs to an in-plane (lateral) electric field remains largely unexplored. We computationally explore spin-mixing interactions in the molecular states of single holes confined in vertically stacked InAs/GaAs QDMs using atomistic tight-binding simulations. We systematically investigate QDMs with different geometric structure parameters and local piezoelectric fields. We observe both a relatively large Stark shift and a change in the Zeeman splitting as the magnitude of the lateral electric field increases. Most importantly, we observe that lateral electric fields induce hole-spin mixing with a magnitude that increases with increasing lateral electric field over a moderate range. These results suggest that applied lateral electric fields could be used to fine tune and manipulate, in situ, the energy levels and spin properties of single holes confined in QDMs.