Using a serrated rib dipped in just enough water so it can be seen wetting the surface, carefully score the left edge of your cup blank. Be careful not to distort or thin the edge of the slab - we just want to give it some tooth so it will grab onto the other side of the lap joint. I don't use slip to join clay. If the slab is at the correct stage of dryness, it will easily join to itself with water only. I do use defloculated water to join porcelain in the summer months, but don't really know if it is necessary.
Now, turn the slab over and score and wet the back side of the right edge, take care not to stretch the edge. The edges should each have approximately the same taper.