Chiral plasmonic nanoantennas manifest a strong asymmetric response to circularly polarized light. Particularly, the geometric handedness of a plasmonic structure can alter the circular polarization state of light emitted from nearby sources, leading to a spin-dependent emission direction. In past experiments, these effects have been attributed entirely to the localized plasmonic resonances of single antennas. In this work we demonstrate that, when chiral nanoparticles are arranged in diffractive arrays, lattice resonances play a primary role in determining the spin-dependent emission of light. We fabricate 2D diffractive arrays of planar chiral metallic nanoparticles embedded in a light-emitting dye-doped slab. By measuring the polarized photoluminescence enhancement we show that the geometric chirality of the array's unit cell induces a preferential circular polarization, and that both the localized surface plasmon resonance and the delocalized hybrid plasmonic-photonic mode contribute to this phenomenon. By further mapping the angle-resolved degree of circular polarization, we demonstrate that strong chiral dissymmetries are mainly localized at the narrow emission directions of the surface lattice resonances. We validate these results against a coupled dipoles model calculation, which correctly reproduces the main features. Our findings demonstrate that, in diffractive arrays, lattice resonances play a primary role into the light spin-orbit effect, introducing a highly non-trivial behavior in the angular spectra.