We describe the formation of lanthanide-organic coordination networks and complexes under ultra-high-vacuum conditions on a clean Ag(100) surface. The structures comprise single Ho atoms as coordination centers and 1,4-benzenedicarboxylate (from terephtalic acid, TPA) as molecular linkers. Using low temperature scanning tunneling microscopy, we find two different chiral phases of surface-supported metal-organic structures incorporating Ho atoms. Density functional theory calculations can explain the structure of both binding motifs and give possible reasons for their varying formation under the respective Ho/TPA ratios, as well as deposition and annealing temperatures. Metal-ligand interactions drive the formation of cloverleaf-shaped mononuclear Ho-TPA(4) complexes establishing supramolecular arrays stabilized through hydrogen bonding. A 2D lanthanide-organic reticulation is observed when changing the stoichiometry between the two building blocks. The combined insights from scanning tunneling microscopy and density functional theory reveal the relative stability, charge transfer, and bonding environment of both motifs.