Models of ligand binding are often based on four assumptions: (1) steric fit: that binding is determined mainly by shape complementarity; (2) native binding: that ligands mainly bind to native states; (3) locality: that ligands perturb protein structures mainly at the binding site; and (4) continuity: that small changes in ligand or protein structure lead to small changes in binding affinity. Using a generalization of the 2D HP lattice model, we study ligand binding and explore these assumptions. We first validate the model by showing that it reproduces typical binding behaviors. We observe ligand-induced denaturation, ANS and heme-like binding, and "lock-and-key" and "induced-fit" specific binding behaviors characterized by Michaelis-Menten or more cooperative types of binding isotherms. We then explore cases where the model predicts violations of the standard assumptions. For example, very different binding modes can result from two ligands of identical shape. Ligands can sometimes bind highly denatured states more tightly than native states and yet have Michaelis-Menten isotherms. Even low-population binding to denatured states can cause changes in global stability, hydrogen-exchange rates, and thermal B-factors, contrary to expectations, but in agreement with experiments. We conclude that ligand binding, similar to protein folding, may be better described in terms of energy landscapes than in terms of simpler mass-action models.