Two series of the LixMn2O4 spinet samples were studied at low temperatures (200-300 K) on electrical, thermal (DSC) and structural (X-ray diffraction (XRD)) properties for different lithium contents. Results obtained for deintercalated spinet samples with x similar to 1 revealed the existence of a broad (100 K) phase transition that can be attributed to the molecular polaron condensation, leading to the orthorhombic distortion of the initial cubic form. The differential scanning calorimetry (DSC) measurement results enable us to regard the phase transition as a form of order-disorder one. Corresponding thermoelectric power (TEP) and electrical conductivity measurements fall within such description, moreover, indicating clear inconsistency between the measured regular DC conductivity of the spinel sample and that observed for the cathode in the working lithium cell. This discrepancy points to an alternative charge transport mechanism existing in the manganese spinet cathode, and it seems to be essential for the lithium cell performance.