The surface structures of copper phthalocyanine (CuPc) thin films deposited on sulphur-passivated and plane perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA)-covered InAs(100) surfaces have been studied by low energy electron diffraction (LEED) and van der Waals (vdW) intermolecular interaction energy calculations. The annealing to $300^{circ}C$ and $450^{circ}C$ of $(NH_4)_2S_x$-treated InAs(100) substrates produces a ($1{ imes}1$) and ($2{ imes}1$) S-passivated surface respectively. The CuPc deposition onto the PTCDA-covered InAs(100) surface leads to a ring-like diffraction pattern, indicating that the 2D ordered overlayer exists and the structure is dominantly determined by the intermolecular interactions rather than substrate-molecule interactions. However, no ordered LEED patterns were observed for the CuPc on S-passivated InAs(100) surface. The intermolecular interaction energy calculations have been carried out to rationalise this structural difference. In the case of CuPc unit cells on PTCDA layer, the planar layered CuPc structure is more stable than the $alpha$-herringbone structure, consistent with the experimental LEED results. For CuPc unit cells on a S-($1{ imes}1$) layer, however, the $alpha$-herringbone structure is more stable than the planar layered structure, consistent with the absence of diffraction pattern. The results show that the lattice structure during the initial stages of thin film growth is influenced strongly by the intermolecular interactions at the interface.