We demonstrate surface-plasmon lasing in hexagonal metal hole arrays with a semiconductor gain medium. The device can be tuned between two laser modes, with distinct wavelengths, spatial distributions, and polarization patterns, by changing the size of the optically pumped area. One of the modes exhibits a six-fold polarization pattern, while the mode observed for larger pump spots has a rotationally symmetric polarization pattern. We explain the mode tuning by the differences of in-plane and radiative out-of-plane losses of the modes. The spatial and polarization properties of the modes are conveniently described by a sum of vectorial orbital angular momentum beams with orbital, spin, and total angular momentum j= l + s.