Self-association of the protein lactoferrin is studied in solution using small-angle X-ray scattering techniques. Effective static structure factors have been shown to exhibit either a monotonic or a nonmonotonic dependence on protein concentration in the small wavevector limit, depending on salt concentration. The behavior correlates with a nonmonotonic dependence of the second virial coefficient on salt concentration, such that a maximum appears in the structure factor at a low protein concentration when the second virial coefficient is negative and close to a minimum. The results are interpreted in terms of an integral equation theory with explicit dimers, formulated by Wertheim, which provides a consistent framework able to explain the behavior in terms of a monomer-dimer equilibrium that appears because of a highly directional patch attraction. Short attraction ranges preclude trimer formation, which explains why the protein system behaves as if it were subject to a concentration-dependent isotropic protein-protein attraction. Superimposing an isotropic interaction, comprising screened Coulomb repulsion and van der Waals attraction, on the patch attraction allows for a semiquantitative modeling of the complete transition pathway from monomers in the dilute limit to monomer-dimer systems at somewhat higher protein concentrations.