Li-rich lithium iron phosphate Li1+δFe1-δPO4 (Li-rich LFP) prepared by the solvothermal method via the Li3PO4 precursor demonstrates excellent electrochemical characteristics such as C-rate capability (140 mAh g-1 at 10 C charge for the Li1.04Fe0.96PO4/C material) and low voltage hysteresis between lithiation and delithiation (14 mV at C/300 rate for the same sample). Phase transformations and evolution of the Fe cations coordination environment during Li+ (de)intercalation are studied in operando regime by means of synchrotron X-ray powder diffraction (SXPD) and 57Fe Mössbauer spectroscopy (MS). The presence of a certain amount of Li+ in the M2 position in the crystal structure of the as-prepared Li-rich LFPs leads to an additional component in the MS spectra corresponding to ferric ions in the M2 position with distorted second coordination sphere. Evolution of the MS spectra during charge/discharge reveals the clear relationship between the relative fraction of this component and the mechanism of Li+ (de)intercalation. Extended single-phase regions with large Li+ nonstoichiometry in the triphylite and heterosite phases of Li1.04-xFe0.96PO4 observed by means of SXPD appear due to Li- Fe defects existing in the as-prepared Li-rich LFPs and acting as a "diluting" agent, which prevents two-phase transition. Increased thermodynamic stability of the intermediate Li1+δ-xFe1-δPO4 solid solutions was also shown by DFT calculations. These features can be regarded as an additional merit of Li-rich LFPs, rendering them promising cathodes for high-power Li-ion batteries.