The lifting of the fourfold degeneracy of the zeroth Landau level in graphene under high magnetic fields has been the subject of numerous experimental studies, and attributed to various mechanisms such as pure spin splitting, spin splitting combined with subsequent valley splitting, or the formation of a quantum Hall insulator. Unexplored, however, is the influence of an energy gap on the quantum Hall effect (QHE) states in graphene. Here we demonstrate, using measurements of the magnetoresistance of graphene antidot lattices (GALs) in magnetic fields up to 30 T and temperatures between 2 and 100 K, that gap opening in these samples is accompanied by valley polarization and a change from linear to parabolic band structure at low carrier energies. The emergence of a massive character of the carriers profoundly alters the transport characteristics of the zeroth Landau level, which manifests itself in a linear increase of the activated gap with magnetic field. Furthermore, samples of the highest quality display spin splitting on top of the valley splitting, albeit of significantly smaller magnitude.