Lytic polysaccharide monooxygenases (LPMOs) are ubiquitous oxidoreductases, facilitating the degradation of polymeric carbohydrates in biomass. Cellobiose dehydrogenase (CDH) is a biologically relevant electron donor in this process, with the electrons resulting from cellobiose oxidation being shuttled from the CDH dehydrogenase domain to its cytochrome domain and then to the LPMO catalytic site. In this work, we investigate the interaction of four Neurospora crassa LPMOs and five CDH cytochrome domains from different species using computational methods. We used HADDOCK to perform protein-protein docking experiments on all 20 combinations and subsequently to select four complexes for extensive molecular dynamics simulations. The potential of mean force is computed for a rotation of the cytochrome domain relative to LPMO. We find that the LPMO loops are largely responsible for the preferred orientations of the cytochrome domains. This leads us to postulate a hybrid version of NcLPMO9F, with exchanged loops and predicted altered cytochrome binding preferences for this variant. Our work provides insight into the possible mechanisms of electron transfer between the two protein systems, in agreement with and complementary to previously published experimental data.