Careful calorimetric and polarization optical studies of a metastable cubic modification of a CsLiCrO4 crystal (space group (\(F\overline 4 3m\))) are performed. Anomalies of the heat capacity indicative of structural distortions at 92.4 and 69.1 K were revealed, and the values of the thermodynamic parameters of the phase transitions were determined. The crystal twinning in the intermediate phase was studied. A comparative analysis of the phase transitions occurring in a series of ALiMO4 crystals (A = NH4, Cs; M = S, Cr, Mo, W) was performed. First studies of the monotropic structural transformation \(F\overline 4 3m\) → Pmcn and the enantiotropic phase transition Pmcn ⇄ P1121/n were carried out using scanning calorimetry, and the thermodynamic parameters of these transitions were determined.