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We present the results from an X-ray variability study of IRAS 13224-3809. This is probably the best source for X-ray reverberation studies since it is X-ray bright, extremely variable, and it has been extensively observed with XMM-Newton. We used all the archival XMM-Newton data from the three EPIC cameras (to increase the signal-to-noise) and, given the many observations of the source, we were able to compute the time-lags spectra in three different flux levels/periods. We fitted the time-lags and energy spectra, simultaneously, using a new X-ray reverberation code which computes the time dependent reflection spectra of the disc as a response to an X-ray flash from a point source located on the axis of the black-hole (BH) accretion disc (lamp-post geometry). To the best of our knowledge, this is the first time for an AGN that both time-lags and energy spectra are fitted by a model simultaneously in different flux periods. The model fits in the case when the BH is rapidly rotating are significantly better than the model fits in the case of a Schwarzschild BH. This result strongly favours the hypothesis of a rotating central BH in this source. We also detect significant variations in the height of the X-ray corona. The X-ray height appears to increase from 3-5 gravitational radii when the X-ray luminosity is of the order of 1.5-3 percent of the Eddington limit, up to 10 gravitational radii, when the luminosity doubles.