Heteroepitaxy of molecular adsorbates on crystalline substrates is used to assess fundamental aspects of layer formation and interaction across the interface. Depositing organic molecules on graphene, for instance, is often stimulated by the desire to noncovalently tune its electronic properties. Here, we study monolayers and bilayers of the near-infrared absorber lead phthalocyanine (PbPc) by means of scanning tunneling microscopy and spectroscopy (STM, STS), low-energy electron diffraction (LEED), and optical differential reflectance spectroscopy (DRS). In an earlier report [Nhung Nguyen, T. T. et al. Phys. Rev. B 2021, 103, L201408], it was claimed that PbPc would form a monolayer structure on highly oriented pyrolytic graphite (HOPG) with adsorbate lattice vectors differing by as much as 10% from those on monolayer graphene. Yet, from our combined LEED and STM analysis on single-crystal graphite and few-layer graphene on SiC(0001), we find that the lattice parameters differ no more than 0.7% among the different substrates. For PbPc bilayers the structural and spectroscopical properties are found to be caused by physical dimerization, i.e., the formation of face-to-face stacked molecules. The electronic interaction with graphite and graphene, however, is interpreted to be rather weak as attested by the PbPc monomer behavior observed for the first monolayer.