  The thickness dependence of the superconducting energy gap $\Delta_{\rm{La}}$
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 at the surface and W/La interface, leading to a
linear decrease of the critical temperature $T_c$ as a function of the inverse
film thickness. For thick, bulk-like films, $\Delta_{\rm{La}}$ and $T_c$ are
40% larger as compared to literature values of dhcp La 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 $T_c$ originates in the superior purity of the samples investigated
here.
