LiCrSe₂ constitutes a recent valuable addition to the ensemble of two-dimensional triangular lattice antiferromagnets. In this work, we present a comprehensive study of the low temperature nuclear and magnetic structure established in this material. Being subject to a strong magnetoelastic coupling, LiCrSe₂ was found to undergo a first order structural transition from a trigonal crystal system (P3^-m1) to a monoclinic one (C2/m) at T_s = 30 K. Such restructuring of the lattice is accompanied by a magnetic transition at T_N = 30 K. Refinement of the magnetic structure with neutron diffraction data and complementary muon spin rotation analysis reveal the presence of a complex incommensurate magnetic structure with a up-up-down-down arrangement of the chromium moments with ferromagnetic double chains coupled antiferromagnetically. The spin axial vector is also modulated both in direction and modulus, resulting in a spin density wave-like order with periodic suppression of the chromium moment along the chains. This behavior is believed to appear as a result of strong competition between direct exchange antiferromagnetic and superexchange ferromagnetic couplings established between both nearest neighbor and next nearest neighbor Cr³⁺ ions. We finally conjecture that the resulting magnetic order is stabilized via subtle vacancy/charge order within the lithium layers, potentially causing a mix of two co-existing magnetic phases within the sample.