A state of permanent, isothermal non-wetting of a solid surface by a normally wetting liquid may be achieved if the surface moves tangentially to a liquid drop that is pressed against it. Surrounding gas is swept into the space between the liquid and solid creating a lubricating film that prevents wetting. The length scales of the drop and the film are typically three or more orders of magnitude different, making numerical simulation difficult from a resolution standpoint. The present paper focuses on a hybrid approach employing lubrication theory for the thinnest portions of the gas film and numerical simulation for the liquid and outer gas phases.