Aperiodic lattices are a promising route to achieving tunable or multi-frequency lasing, but their threshold spectrum remains largely unstudied. We find that holographically designed aperiodic lattices can possess a multimode spectral response, containing both defect and band-edge photonic states. Under the influence of facet feedback the aperiodic lattice maintains remarkable spectral control at multiple frequencies over a wide bandwidth. This control arises from enhancement to the photon density of states at the designed frequencies, reducing the threshold of modes in the Fabry Perot coupled aperiodic lattice laser. Our results suggest that aperiodic lattice lasers are robust against fabrication imperfections, as exemplified by experimental demonstrations in prior work.