Crystal structures of Li2MO3 (M=Sn, Ti) and TiO(OH)2 have been studied in detail and refined using X-ray powder diffraction data. All compounds posses a high concentration of defects in the structure. The crystal structures of the Li2MO3 salts obtained at 700°C reveal stacking faults of LiM2 metal layers, which leads to the appearance of short-range order in three possible space groups: C2/c, C2/m, P3112. The possibility to stabilize this imperfect state increases the mobility of the Li+ ions in the Li2TiO3 structure and allows the complete exchange of lithium by hydrogen in acid water solutions with formation of TiO(OH)2. The crystal structure of TiO(OH)2 belongs to the layered double hydroxide structure type with the 3R1 sequence of oxygen layers and can be described as a stacking of charge-neutral metal oxyhydroxide slabs [(OH)2OTi2O(OH)2].