We report a combined synchrotron X-ray and neutron diffraction study on as-grown La2CoO4.14 single-crystal from 10 to 470 K. Unprecedented structural features in terms of a (3 + 2)D incommensurate modulation have been detected and characterized in the Low Temperature Orthorhombic (LTO) phase already at room temperature despite the complex twinning that was unravelled. A new intermediate phase between the LTO and High Temperature Tetragonal (HTT) phases has been observed for the first time (in the range of 413-433 K). The transformation from LTO to this so-called HTLO (High Temperature Less Orthorhombic) phase is associated to a lowering of orthorhombicity and a loss of one modulation vector, yielding a (3 + 1)D incommensurate modulation. Conversely, above 433 K the HTT phase appears as nonmodulated but exhibits a strong dynamic disorder of CoO6 octahedra, which has been characterized in detail by reconstruction of nuclear densities via the Maximum Entropy Method (MEM).