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We studied X-ray reverberation lags in the BHXRB GX 339-4 at the end of the2014-2015 outburst. We analysed data from a XMM-Newton campaign covering theend of the transition from the soft to the hard state, and the decrease ofluminosity in the hard state. During all the observations we detected, at highfrequencies, significant disc variability, responding to variations of thepower law emission with an average time delay of $\sim0.009\pm 0.002$ s. Thesenew detections of disc thermal reverberation add to those previously obtainedand suggest the lag to be always present in hard and hard-intermediate states.Our study reveals a net decrease of lag amplitude as a function of luminosity.We ascribe this trend to variations of the inner flow geometry. A possiblescenario implies a \emph{decrease} of the inner disc truncation radius as theluminosity increases at the beginning of the outburst, followed by an\emph{increase} of the inner disc truncation radius as the luminosity decreasesat the end of the outburst. Finally, we found hints of FeK reverberation($\sim3\sigma$ significance) during the best quality observation of the XMMmonitoring. The lag at the FeK energy has similar amplitude as that of thethermally reprocessed component, as expected if the same irradiated region ofthe disc is responsible for producing both the thermalized and reflectedcomponent. This finding suggests FeK reverberation in BHXRBs to be at the reachof current detectors provided observations of sufficiently long exposure areavailable.

Evolution of the reverberation lag in GX 339-4 at the end of an outburst