  Rapid temporal variability has been widely observed in the light curves of
gamma-ray bursts (GRBs). One possible mechanism for such variability is related
to the relativistic eddies in the jet. In this paper, we include the
contribution of the inter-eddy medium together with the eddies to the gamma-ray
emission. We show that the gamma-ray emission can either lead or lag behind the
observed synchrotron emission, where the latter originates in the inter-eddy
medium and provides most of seed photons for producing gamma-ray emission
through the inverse-Compton scattering. As a consequence, we argue that the
lead/lag found in non-stationary short-lived light curves may not reveal the
intrinsic lead/lag of different emission components. In addition, our results
may explain the lead of gamma-ray emission with respect to optical emission
observed in GRB 080319B.
