  We study the physics potential of the long-baseline experiments T2HK, T2HKK
and ESS$\nu$SB in the context of invisible neutrino decay. We consider normal
mass ordering and assume that the state $\nu_{3}$ as unstable, decaying into
sterile states during the flight and obtain constraints on the neutrino decay
lifetime ($\tau_3$). We find that T2HK, T2HKK and ESS$\nu$SB are sensitive to
the decay-rate of $\nu_{3}$ for $\tau_{3}/m_{3} \leq 2.72\times10^{-11}$s/eV,
$\tau_{3}/m_{3} \leq 4.36\times10^{-11}$s/eV and $\tau_{3}/m_{3} \leq
2.43\times10^{-11}$s/eV respectively at 3$\sigma$ C.L. We compare and contrast
the sensitivities of the three experiments and specially investigate the role
played by the mixing angle $\theta_{23}$. It is seen that for experiments with
flux peak near the second oscillation maxima, the poorer sensitivity to
$\theta_{23}$ results in weaker constraints on the decay lifetime. Although,
T2HKK has one detector close to the second oscillation maxima, having another
detector at the first oscillation maxima results in superior sensitivity to
decay. In addition, we find a synergy between the two baselines of the T2HKK
experiment which helps in giving a better sensitivity for $\theta_{23}$ in the
higher octant. We discuss the octant sensitivity in presence of decay and show
that there is an enhancement in sensitivity which occurs due to the
contribution from the survival probability $P_{\mu\mu}$ which is more
pronounced for the experiments at the second oscillation maxima. We also obtain
the combined sensitivity of T2HK+ESS$\nu$SB and T2HKK+ESS$\nu$SB as
$\tau_{3}/m_{3} \leq 4.36\times10^{-11}$s/eV and $\tau_{3}/m_{3} \leq
5.53\times10^{-11}$s/eV respectively at 3$\sigma$ C.L.
