The field of organic electronics is flourishing amidst applications in the entertainment and energy sectors which are based on stacks of different organic materials. Each layer or interface between layers serves a special purpose, such as injection, extraction, transport, and blocking of charge carriers. While in industrial applications polycrystalline films are often more cost-effective, it is films with a high degree of long-range order that excel in performance since low molecular order and grain boundaries reduce the charge carrier mobility. Therefore, it is important to characterize and understand the ordered growth, i.e., the epitaxy, of molecular layers. The reproducible orientation of an ordered molecular layer on a crystalline substrate can often be understood within the framework of lattice epitaxy, where the adsorbate and the substrate share common sets of lattice planes. This includes subtler types of epitaxy than simply commensurate, i.e., identical lattices. This work aims to improve the experimental determination and characterization of epitaxy types in these non-commensurate cases, using low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM), as well as the understanding of the mechanisms driving the epitaxy. It is discussed which implications for LEED arise from structural modulations in non-commensurate epitaxial layers. For this, a theoretical treatment in the form of a simplified structure factor allows for a quite intuitive and helpful insight into an otherwise complicated diffraction theory of modulated structures. This allows for the verification and explanation of the incommensurate epitaxy of hexa-peri-hexabenzocoronene adsorbed on graphite. Comparing first-principles-based calculations with experimental results, it is unequivocally shown that the system represents an example of orientational epitaxy. Moreover, the findings constitute the first direct prove of static lattice distortions leading to this type of epitaxy.