We propose to use collective lattice resonances in plasmonic nanoparticle arrays to enhance and tailor photoelectron emission in Schottky barrier photodetectors and solar cells. We show that the interaction between narrow-band lattice resonances (the Rayleigh anomaly) and broader-band individual-particle excitations (localized surface plasmon resonances) leads to stronger local field enhancement. In turn, this causes a significant increase of the photocurrent compared to the case when only individual-particle excitations are present. The results can be used to design new photodetectors with highly selective, tunable spectral response, which are able to detect photons with the energy below the semiconductor bandgap. The findings can also be used to develop solar cells with increased efficiency.