Powder x-ray diffraction has been performed on lithium sulphate, Li 2 SO 4 , in the temperature range 300 to 1000 K and at pressures up to 7.5 GPa. The ambient pressure  phase appears stable up to 3 GPa, whereupon a slow transformation begins into a new phase, ␦-Li 2 SO 4 . This phase is characterized by broad, very low intensity Bragg peaks. Above 7 GPa and with slight heating, another phase, ⑀-Li 2 SO 4 , is formed which shows sharp Bragg peaks. Rietveld refinement of the structure of the ⑀ phase has shown it to be isostructural to the high-temperature phase III of Na 2 SO 4 . Molecular dynamics simulations of the ⑀ phase using an established potential indicate disordering of the lithium ions and rotations of the sulphate groups at high temperature, but not at a level approaching the extreme disordering shown in the superionic ␣ form of Li 2 SO 4 .