Endohedrally encapsulated hydrogen clusters doped with inert helium (H24He) and ionic lithium (H24Li(+)) are investigated. The confinement model is a nanoscopic analogue of the experimental compression of solid hydrogen. The structural and electronic properties of the doped hydrogen clusters are determined under the effects of pressure. The results are compared with these of the isoelectronic (pure) hydrogen counterpart H26 under similar physical conditions. Pressure increase rates with respect to H26 of approximately 1.1 are observed with the insertion of helium or lithium. The changes of geometrical structures and HOMO-LUMO gap energies with the pressure point out the pressure-induced metallization of the Li(+)-doped cluster. The computations are done using density functional theory in the form implemented for molecules; they include zero-point energy effects and, to our best knowledge, are the first of their kind.