Periodic dielectric structures are typically integrated with a planar waveguide to create photonic band-edge modes for feedback in one-dimensional distributed feedback lasers and two-dimensional photonic-crystal lasers(1-4). Although photonic band-edge lasers are widely used in optics and biological applications, drawbacks include low modulation speeds and diffraction-limited mode confinement(5,6). In contrast, plasmonic nanolasers can support ultrafast dynamics and ultrasmall mode volumes(7-9). However, because of the large momentum mismatch between their nanolocalized lasing fields and free-space light, they suffer from large radiative losses and lack beam directionality. Here, we report lasing action from band-edge lattice plasmons in arrays of plasmonic nanocavities in a homogeneous dielectric environment. We find that optically pumped, two-dimensional arrays of plasmonic Au or Ag nanoparticles surrounded by an organic gain medium show directional beam emission (divergence angle <1.5 degrees and linewidth <1.3 nm) characteristic of lasing action in the far-field, and behave as arrays of nanoscale light sources in the near-field. Using a semi-quantum electromagnetic approach to simulate the active optical responses, we show that lasing is achieved through stimulated energy transfer from the gain to the band-edge lattice plasmons in the deep subwavelength vicinity of the individual nanoparticles. Using femtosecond-transient absorption spectroscopy, we verified that lattice plasmons in plasmonic nanoparticle arrays could reach a 200-fold enhancement of the spontaneous emission rate of the dye because of their large local density of optical states.