We report a dye-doped nematic liquid crystal microlaser that allows the two-dimensional alignment of the liquid crystal to be projected directly on the output polarization of the laser beam. The laser cavity is composed of a pair of dielectric multilayers sandwiching a dye-doped nematic liquid crystal with patterned alignment, and exploits the fact that the resonance modes in such systems are split into two orthogonally polarized modes experiencing either the extraordinary or ordinary refractive index of the liquid crystal. Azimuthally polarized lasing is demonstrated using a concentrically aligned liquid crystal layer.