Lignin and cellulose are two of the most abundant polymers on Earth, and are found in close proximity within plant cell walls. Despite their ubiquity, relatively little is known quantitatively about their interactions within plants, and by extension how their interaction may affect industrial biomass utilization. Given the inherent heterogeneity of the lignin polymer and the structural complexity of cellulose, quantitative relationships between given cellulose faces and specific lignin chemistries have been challenging to ascertain experimentally. In this study, we use molecular simulation to examine individual combinations of cellulose binding face and lignin chemistry to build a quantitative lignin-cellulose interaction atlas, including contributions from both specific hydrogen bonds observed in simulation and nonspecific interactions between lignin and cellulose driven by solvent considerations. Over all monomeric and dimeric lignin chemistries tested, the hydrophobic 100 face is the preferred cellulose interaction site. Among the hydrophilic crystalline faces, binding of these molecules is strongest to the 110 cellulose face. The chemical composition of lignin monomers and dimers is also found to modulate the binding affinity, with additional methoxy groups increasing the contact area to the cellulose surface, which we hypothesize may protect native cellulose from degradation. Additional methoxylation and monomer linkages that facilitate planar aromatic ring orientations increase the binding affinity between small lignin-related molecules and cellulose, with the planar linkages between guaiacyl-type monomers leading to higher binding affinities. These trends can be extended to larger lignin polymers, where we quantify the relationships between lignin polymer size and binding affinity through replica exchange umbrella sampling simulations. Rather than molecular weight, the binding surface area between the lignin polymer and the cellulose surface dictates the interaction strength. As a result, based on the findings here, we expect there to be abundant and durable interaction between cellulose and lignin, particularly on the hydrophobic face of cellulose where cellulase enzymes typically bind.