The thickness dependence of the superconducting energy gap ΔLa of double hexagonally close packed (dhcp) lanthanum islands grown on W(110) is studied by scanning tunneling spectroscopy, from the bulk to the thin-film limit. Superconductivity is suppressed by the boundary conditions for the superconducting wavefunction on the surface and W/La interface, leading to a linear decrease of the critical temperature Tc as a function of the inverse film thickness. For the thick, bulk-like films, ΔLa and Tc are 40% larger compared to the literature values of dhcp La as measured by other techniques. This finding is reconciled by examining the effects of surface contamination as probed by modifications of the surface state, suggesting that the large Tc originates in the superior purity of the samples investigated here.