The structure of oxygen-intercalated La(2)CuO(4.07) has been investigated at 20 and 300 K by neutron diffraction on an electrochemically oxidized single crystal. At 20 K, reconstruction of the nuclear density by maximum entropy method shows strong displacements of the apical oxygen atoms towards [100] with respect to the F-centred unit cell, whilst displacements towards [110] and [100] were both found to be present at ambient temperature. Combining structural studies with first-principles lattice dynamical calculations, we interpret the displacements of the apical oxygen atoms to be at least partially of dynamic origin already at ambient temperature. Strong displacements of the apical oxygen atoms of stoichiometric and oxygen-doped La(2)CuO(4+delta) and corresponding associated lattice instabilities, i.e. low-energy phonon modes, are considered as a general prerequisite of low-temperature oxygen diffusion mechanisms. Lattice dynamical calculations on La(2)CuO(4+delta) suggest that the oxygen species diffusing at low temperature are not the interstitial but, more prominently, the apical oxygen atoms. The presence of interstitial oxygen atoms is, however, important to amplify via specific, low-energy phonon modes, a dynamic exchange mechanism between apical and vacant interstitial oxygen sites, thus allowing a dynamically triggered, shallow potential oxygen diffusion pathway. The crucial role of lattice dynamics to enable low-temperature oxygen mobility in K(2)NiF(4)-type oxides is discussed on a microscopic scale and compared to similar low-temperature oxygen diffusion mechanisms, recently proposed for non-stoichiometric oxides with Brownmillerite-type structure.< Réduire