We study lasing in distributed feedback lasers made from square lattices of silver particles in a dye-doped waveguide. We present a systematic analysis and experimental study of the band structure underlying the lasing process as a function of the detuning between the particle plasmon resonance and the lattice Bragg diffraction condition. To this end, as gain medium we use either a polymer doped with Rh6G only, or polymer doped with a pair of dyes (Rh6G and Rh700) that act as a Förster energy transfer (FRET) pair. This allows for gain, respectively, at 590 or 700 nm when pumped at 532 nm, compatible with the achievable size tunability of silver particles embedded in the polymer. By polarization-resolved spectroscopic Fourier microscopy, we are able to observe the plasmonic/photonic band structure of the array, unraveling both the stop gap width, as well as the loss properties of the four involved bands at fixed lattice Bragg diffraction condition and as a function of detuning of the plasmon resonance. To explain the measurements we derive an analytical model that sheds insights on the lasing process in plasmonic lattices, highlighting the interaction between two competing resonant processes, one localized at the particle level around the plasmon resonance, and one distributed across the lattice. Both are shown to contribute to the lasing threshold and the overall emission properties of the array.