I use the method of classical density-functional theory in the weighted-densityapproximation of Tarazona to investigate the phase diagram and the interface structure ofa two-dimensional lattice-gas model with three phases—vapour, liquid and triangular solid.While a straightforward mean-field treatment of the interparticle attraction is unable togive a stable liquid phase, the correct phase diagram is obtained when including a suitablychosen square-gradient term in the system grand potential. Taking this theory for granted,I further examine the structure of the solid–vapour interface as the triple point isapproached from low temperature. Surprisingly, a novel phase (rather than the liquid) isfound to grow at the interface, exhibiting an unusually long modulation alongthe interface normal. The conventional surface-melting behaviour is recoveredonly by artificially restricting the symmetries being available to the density field.