The three-dimensional charge density wave (CDW) compound Lu 2 Ir 3 Si 5 undergoes a first-order CDW phase transition at around 200 K. An atypical CDW state is found, that is characterized by an incommensurate CDW with q = [0.2499(3), 0.4843(4), 0.2386(2)] at 60 K, and a large orthorhombic-to-triclinic lattice distortion with β = 91.945(2) • . We present the modulated crystal structure of the incommensurate CDW state. Structural analysis shows that the CDW resides on the zigzag chains of iridium atoms along c. The structural distortions are completely similar between nonmagnetic Lu 2 Ir 3 Si 5 and previously studied isostructural magnetic Er 2 Ir 3 Si 5 with the small differences explained by the different values of the atomic radii of Lu and Er. Such a similarity is unique to R 2 Ir 3 Si 5 (R = rare earth). It differs from, for example, the rare-earth CDW compounds R 5 Ir 4 Si 10 for which Lu 5 Ir 4 Si 10 and Er 5 Ir 4 Si 10 possess entirely different CDW states. We argue that the mechanism of CDW formation, thus, is different for R 2 Ir 3 Si 5 and R 5 Ir 4 Si 10 .