  We studied X-ray reverberation lags in the BHXRB GX 339-4 at the end of the
2014-2015 outburst. We analysed data from a XMM-Newton campaign covering the
end of the transition from the soft to the hard state, and the decrease of
luminosity in the hard state. During all the observations we detected, at high
frequencies, significant disc variability, responding to variations of the
power law emission with an average time delay of $\sim0.009\pm 0.002$ s. These
new detections of disc thermal reverberation add to those previously obtained
and 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 possible
scenario implies a \emph{decrease} of the inner disc truncation radius as the
luminosity increases at the beginning of the outburst, followed by an
\emph{increase} of the inner disc truncation radius as the luminosity decreases
at the end of the outburst. Finally, we found hints of FeK reverberation
($\sim3\sigma$ significance) during the best quality observation of the XMM
monitoring. The lag at the FeK energy has similar amplitude as that of the
thermally reprocessed component, as expected if the same irradiated region of
the disc is responsible for producing both the thermalized and reflected
component. This finding suggests FeK reverberation in BHXRBs to be at the reach
of current detectors provided observations of sufficiently long exposure are
available.
