  For a sample of Swift and Fermi GRBs, we show that the minimum variability
timescale and the spectral lag of the prompt emission is related to the bulk
Lorentz factor in a complex manner: For small $\Gamma$'s, the variability
timescale exhibits a shallow (plateau) region. For large $\Gamma$'s, the
variability timescale declines steeply as a function of $\Gamma$ ($\delta
T\propto\Gamma^{-4.05\pm0.64}$). Evidence is also presented for an intriguing
correlation between the peak times, t$_p$, of the afterglow emission and the
prompt emission variability timescale.
