The locus of lines in Q leading generically to marked numerical Godeaux surfaces with torsion group ℤ/3 is birational to a ℙ1-bundle Z over ℙ3 × ℙ1. The procedures gives two parametrization homomorphisms from Sa to the coordinate ring of Z, where the image of each map gives a point in Q whose connecting line is completely contained in Q and leads generically to a ℤ/3-Godeaux surface.