Plasmonic nanoparticles lattices in a dielectric environment demonstrate exceptional optical properties due to the combination of plasmonic structures' ability to confine light in deep subwavelength scale and dielectric ones to support high-quality optical modes. However, such structures, especially in the case of the small size of plasmonic particles, are hard for the calculation by the means of the Fourier modal method (FMM) specialized for periodic structures, since their local field is described by high-k|| harmonics. We propose not to account for a large number of harmonics, but to consider the lattice in discrete dipole approximation (DDA) to construct its scattering matrix. In this work, we apply this approach for lattices with several particles in a cell. The performance of the method is demonstrated on an example of the lattice on a waveguide that supports polarization controlled coupling of circularly polarized light to guided modes propagating in opposite directions. We show the high speed and precision of our approach, which allows us to use it both for the calculation of plasmonic lattices spectra and the design of nanophotonic devices based on such lattices.