  The LHCb measurement of the lifetime ratio of the $\Lambda^0_b$ to the
$\overline{B}^0$ meson is updated using data corresponding to an integrated
luminosity of 3.0 fb$^{-1}$ collected using 7 and 8 TeV centre-of-mass energy
$pp$ collisions at the LHC. The decay modes used are $\overline{B}^0\to J/\psi
p K^-$ and $\overline{B}^0\to J/\psi \pi^+ K^-$, where the $\pi^+K^-$ mass is
consistent with that of the $\overline{K}^{*0}(892)$ meson. The lifetime ratio
is determined with unprecedented precision to be $0.974\pm0.006\pm0.004$, where
the first uncertainty is statistical and the second systematic. This result is
in agreement with original theoretical predictions based on the heavy quark
expansion. Using the current world average of the $\overline{B}^0$ lifetime,
the $\Lambda^0_b$ lifetime is found to be $1.479 \pm 0.009 \pm 0.010$ ps.
