Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave dynamics and geometric optics in resonators. However, the mode structures of three-dimensional microlasers without rotational symmetry remain largely unexplored due to fabrication limitations. Previous studies of such cavities revealed lasing modes localized on periodic orbits exclusively confined to a single plane. In this work, we report on the characterization of pyramidal, polymer-based microlasers and demonstrate that the lasing modes are localized on a genuine three-dimensional periodic orbit. The consequences on the laser features are further discussed, in particular stability and polarization issues.