We investigate the effects of lattice structure on the properties of photonic-crystal surface-emitting lasers. We analyze a general type of crystalline geometry known as the centered-rectangular lattice, which includes both square and triangular lattices. We theoretically and experimentally investigate the laser cavity characteristics of devices based on such photonic crystals, including the band structure and beam patterns, in order to explore the feasibility of two-dimensional (2D) lasing oscillation. The more general type of crystalline geometry represented by the centered-rectangular lattice should enable a comprehensive understanding of the 2D cavity characteristics to be achieved and also lead to further possibilities in the field of 2D photonic-crystal lasers.