The quasi-2D Pt-based rare earth intermetallic material LaPt2Si2 has attracted attention as it exhibits strong interplay between charge density wave (CDW) and and superconductivity (SC). However, the most of the results reported on this material come from theoretical calculations, preliminary bulk investigations and powder samples, which makes it difficult to uniquely determine the temperature evolution of its crystal structure and, consequently, of its CDW transition. Therefore, the published literature around LaPt2Si2 is often controversial. In this paper, we clarify the complex evolution of the crystal structure, and the temperature dependence of the development of density wave transitions, in good quality LaPt2Si2 single crystals, with high resolution synchrotron X-ray diffraction data. According to our findings, on cooling from room temperature LaPt2Si2 undergoes a series of subtle structural transitions which can be summarised as follows: second order commensurate tetragonal (P4/nmm)-to-incommensurate structure followed by a first order incommensurate-to-commensurate orthorhombic (Pmmn) transition and then a first order commensurate orthorhombic (Pmmn)-to-commensurate tetragonal (P4/nmm). The structural transitions are accompanied by both incommensurate and commensurate superstructural distortions of the lattice. The observed behavior is compatible with discommensuration of the CDW in this material.