We study the energy-dependent time lags and rms fractional amplitude of the kilohertz quasi-periodic oscillations (kHz QPOs) of a group of neutron-star low mass X-ray binaries (LMXBs). We find that for the lower kHz QPO the slope of the best-fitting linear model to the time-lag spectrum and the total rms amplitude integrated over the 2 to 25 keV energy band both decrease exponentially with the luminosity of the source. For the upper kHz QPO the slope of the time-lag spectrum is consistent with zero, while the total rms amplitude decreases exponentially with the luminosity of the source. We show that both the slope of the time-lag spectrum and the total rms amplitude of the lower kHz QPO are linearly correlated with a slope of ~1. Finally, we discuss the mechanism that could be responsible for the radiative properties of the kHz QPOs, with the variability originating in a Comptonising cloud or corona that is coupled to the innermost regions of the accretion disc, close to the neutron star.
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