Periodic lattices of strongly scattering objects coupled to active media are of central importance in applied nanophotonics, serving as light-emitting metasurfaces of tailored emission properties and promising an attractive platform for testing novel physical concepts and realization of unprecedented light-shaping functions. We provide an overview of the semianalytical Green function method with Ewald lattice summation applied to the investigation of surface lattice resonances in periodic arrays of resonant nanoscatterers with gain and loss. This theory is meant as a minimal model for plasmonic lattices and metasurfaces with gain: minimal in complexity, yet sufficiently rich to be a self-consistent, fully retarded multiple scattering model. It enables to include the electromagnetic interactions between electric and/or magnetic point dipoles of arbitrary orientation and arrangement, taking into account retardation and tensorial nature of these interactions and including radiation damping. It gives access to the far-field observables (reflection/transmission), as well as to the photonic band structure of guided modes. At the same time, it does not violate the optical theorem, as opposed to the commonly used tight-binding or quasi-static models. After extending the lattice Green function formalism to include gain and loss in the unit cell, we demonstrate the effects of parity-time (PT) symmetry breaking in active-lossy plasmonic arrays: the emergence of exceptional points, nontrivial topology of photonic bands, diverging effective unit-cell polarizability, and spin polarization in the PT-broken phase.