The stratification of acoustic oscillations through the solar photosphere in Lagrangian (comoving) coordinates has been evaluated from a quasi-NLTE inversion of the radiative transfer equation (RTE) applied to a temporal sequence of K I 7699 Å line spectra. The stratifications of amplitude and phase of the temperature and line-of-sight (LOS) velocity Lagrangian oscillations have been evaluated. Our results suggest that, to first order, the photosphere moves up and down as a whole with amplitudes ranging from ~8 km in deep layers (around 0 km) to ~19 km in the upper layers (around 640 km). Numerous short-lived, local temperature and velocity amplitude enhancements in medium-high layers are observed, together with an asymmetric waveform in the oscillation of these two physical quantities. Two nodes are clearly seen in the Lagrangian temperature oscillation run, which are associated with sharp phase jumps of about 180°. The velocity amplitude shows the well known increase with geometrical height, keeping practically in phase.