We study two-dimensional excitons confined in a lattice potential, for high fillings of the lattice sites. We show that a quasicondensate is possibly formed for small values of the lattice depth, but for larger ones the critical phase-space density for quasicondensation rapidly exceeds our experimental reach, due to an increase of the exciton effective mass. On the other hand, in the regime of a deep lattice potential where excitons are strongly localized at the lattice sites, we show that an array of phase-independent quasicondensates, different from a Mott insulator, is realized.