A first principle study of lead adsorption on the pseudo-10-fold surface of the orthorhombic Al13Co4 intermetallic compound has been performed using four possible structural models as substrate. Coverage between atomic adsorption to near 0.08 atm./Å2 has been considered. Relative adsorption energies of Pb atoms on different surface sites in addition with simulated scanning tunneling microscopy images were obtained for each model. Our ab initio calculations demonstrate that the experimental results published recently, highlighting (i) the presence of a preferential adsorption site and (ii) the formation of Pb rows extending along the [010] direction [N. J. Phys. 2011, 13, 10301114] can be only reproduced using a dense Al-rich termination as the substrate structural model. This result confirms the previously established structural model for the (100) surface of orthorhombic Al13Co4 [Phys. Rev. B 2011, 84, 085411]. This study then provides an understanding of the experimental observations for the different lead coverages.