Anionic dimyristoylphosphatidic acid monolayers spread on LaCl3 solutions reveal strong cation adsorption and a sharp transition to surface overcharging at unexpectedly low bulk salt concentrations. We determine the surface accumulation of La3+ with anomalous x-ray reflectivity and find that La3+ compensates the lipid surface charge by forming a Stern layer with approximately 1 La3+ ion per 3 lipids below a critical bulk concentration, ct approximately 500 nM. Above ct, the surface concentration of La3+ increases to a saturation level with approximately 1 La3+ per lipid, thus implying that the total electric charge of the La3+ exceeds the surface charge. This overcharge is observed at approximately 4 orders of magnitude lower concentration than predicted in ion-ion correlation theories. We suggest that transverse electrostatic correlations between mobile ions and surface charges (interfacial Bjerrum pairing) may contribute to the charge inversion.