The self-consistent density response of an electron system is studied in a two-dimensional ͑2D͒ lateral superlattice ͑SL͒ with spin-orbit interaction ͑SOI͒. Under the effect of the lateral periodic potential, the single-electron 2D states are broadened into minibands that are spin split by SOI. In the case of a single fully occupied miniband, we calculate the long-wavelength limit of the polarization function for intraband transi-tions, within the random-phase approximation at T=0 K, and identify the plasmonic dispersion relation in the effective-mass approximation. The interplay between band effects and SOI coupling, considered here to be linear in the electron momentum ͑Rashba͒, is shown to generate a highly anisotropic collective excitation spectrum. If the plasmon propagating perpendicular on the superlattice axis has the characteristic frequency of the quasi-one-dimensional system weakly modified by the SOI split, the one propagating along the SL axis is enhanced by the SOI that couples, through its dependence on the periodic momentum of a Bloch electron, density fluctuations in different layers of the superlattice. The excitation frequency of this mode is found to depend on the miniband width and the amplitude of the SOI coupling constant.