  We performed measurements of switching current distribution in a submicron
La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) intrinsic Josephson junction (IJJ) stack in a
wide temperature range. The escape rate saturates below approximately 2\,K,
indicating that the escape event is dominated by a macroscopic quantum
tunneling (MQT) process with a crossover temperature $T^{*}\approx2\,$K. We
applied the theory of MQT for IJJ stacks, taking into account dissipation and
the phase re-trapping effect in the LSCO IJJ stack. The theory is in good
agreement with the experiment both in the MQT and in the thermal activation
regimes.
