Results from first-principles investigations of the energetical, structural, electronic, and vibrational properties of model structures probing the metal-rich region of the lanthanum-hydrogen system, i.e., the region of the solid solution of hydrogen in lanthanum, are presented. We have studied the site preference and the ordering tendency of hydrogen atoms interstitially bonded in close-packed lanthanum. Spatially separated hydrogen atoms have turned out to exhibit an energetical preference for the occupation of octahedral interstitial sites at low temperature. Indications for a reversal of the site preference in favor of the occupation of tetrahedral interstitial sites at elevated temperature have been found. Linear arrangements consisting of pairs of octahedrally and/or tetrahedrally coordinated hydrogen atoms collinearly bonded to a central lanthanum atom have turned out to be energetically favorable structure elements. Further stabilization is achieved if such hydrogen pairs are in turn linked together so that extended chains of La-H bonds are formed. Pair formation and chain linking counteract the energetical preference for octahedral coordination observed for separated hydrogen atoms.