An improved DMT adhesion model is used in conjunction with an elastoplastic contact model to analyze the adhesion of contacting rough solid surfaces covered with extremely thin layers of a lubricant having a very high affinity for the surfaces. This we call sub-boundary lubrication. The paper investigates the effects of the solid surface topography and the film thickness of the lubricant on the adhesion and pull-off forces. A roughness-dependent critical thickness phenomenon is predicted: very rough surfaces may exhibit low adhesion for a wide range of lubricant thicknesses, while for smooth surfaces adhesion may increase dramatically even for a film thickness t below the standard deviation of surface heights σ. The increased adhesion could cause the surfaces to stick together to the extent that sensitive tribological systems may be damaged.